An Invitation to Modern Number Theory

Give us 5 minutes and we will show you the best book to read today. This is it, the an invitation to modern number theory that will be your best choice for better reading book. Your five times will not spend wasted by reading this website. You can take the book as a source to make better concept. Referring the books that can be situated with your needs is sometime difficult. But here, this is so easy. You can find the best thing of book that you can read.

[1]  R. Durrett.  Probability: Theory and Examples , 1993 .

[2]  Alexandru Zaharescu,et al.  The distribution of spacings between fractional parts of lacunary sequences , 1999 .

[3]  K Ramachandra,et al.  Lectures on transcendental numbers , 1969 .

[4]  S. Simon,et al.  Eigenvalue density of correlated complex random Wishart matrices. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  J. Spencer,et al.  The Elementary Proof of the Prime Number Theorem , 2009 .

[6]  Richard E. Crandall,et al.  On the $‘‘3x+1”$ problem , 1978 .

[7]  Karel Hrbacek,et al.  Introduction to Set Theory , 1978 .

[8]  Jean-Pierre Serre.  A Course in Arithmetic , 1973 .

[9]  N. Wormald,et al.  Models of the , 2010 .

[10]  Herman J. J. te Riele,et al.  On the sign of the difference $\pi(x)-{\rm li}(x)$ , 1987 .

[11]  Dorian Goldfeld,et al.  The Elementary Proof of the Prime Number Theorem: An Historical Perspective , 2004 .

[12]  Paul R. Chernoff,et al.  Pointwise Convergence of Fourier Series , 1980 .

[13]  R. C. Vaughan,et al.  Waring ’ s Problem : A Survey , 2002 .

[14]  Dorian Goldfeld,et al.  The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer , 1976 .

[15]  B. Simon.  The Classical Moment Problem as a Self-Adjoint Finite Difference Operator , 1998, math-ph/9906008.

[16]  Tim Novikoff.  Asymptotic Behavior of the Random 3-Regular Bipartite Graph , 2002 .

[17]  Jeffrey Shallit,et al.  Folded continued fractions , 1992 .

[18]  Edward B. Burger.  Exploring the Number Jungle: A Journey into Diophantine Analysis , 2000 .

[19]  K. Soundararajan.  Small gaps between prime numbers: The work of Goldston-Pintz-Yildirim , 2006 .

[20]  J. Keiper,et al.  Power series expansions of Riemann’s function , 1992 .

[21]  J. H. Conway.  The Weird and Wonderful Chemistry of Audioactive Decay , 1987 .

[22]  Steven J. Miller,et al.  Density Functions for Families of Dirichlet Characters , 2005 .

[23]  J. Hull.  Options, Futures, and Other Derivatives , 1989 .

[24]  Trevor D. Wooley,et al.  Large improvements in Waring's problem , 1992 .

[25]  F. Su.  The Banach-Tarski Paradox , 1990 .

[26]  Nicholas M. Katz,et al.  Random matrices, Frobenius eigenvalues, and monodromy , 1998 .

[27]  Amir D. Aczel.  Fermat's Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem , 1996 .

[28]  Theodor Estermann.  Introduction to modern prime number theory , 1952 .

[29]  G. H. Hardy,et al.  Some problems of 'Partitio numerorum'; I: A new solution of Waring`s problem , 1920 .

[30]  P. Shiu,et al.  PI AND THE AGM A Study in Analytic Number Theory and Computational Complexity (Canadian Mathematical Society Series of Monographs and Advanced Texts) , 1988 .

[31]  William E. Boyce,et al.  Elementary differential equations and boundary value problems - Fourth edition , 1986 .

[32]  I. P. Kornfelʹd,et al.  Ergodic Theory , 1963 .

[33]  Z. Rudnick,et al.  The distribution of spacings between quadratic residues , 1999 .

[34]  Peter Sarnak,et al.  The Pair Correlation Function of Fractional Parts of Polynomials , 1998 .

[35]  Lauwerens Kuipers,et al.  Uniform distribution of sequences , 1974 .

[36]  P. Sarnak.  Some Applications of Modular Forms , 1990 .

[37]  Brian Hayes,et al.  The Spectrum of Riemannium , 2003, American Scientist.

[38]  Nina C Snaith,et al.  Random matrices and L-functions , 2003 .

[39]  Filip Saidak.  A New Proof of Euclid's Theorem , 2006, Am. Math. Mon..

[40]  G. B.,et al.  A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: with an introduction to the Problem of Three Bodies , 1918, Nature.

[41]  H. J. Arnold.  Introduction to the Practice of Statistics , 1990 .

[42]  Joseph H. Silverman,et al.  Diophantine Geometry: An Introduction , 2000 .

[43]  Jonathan Reynolds,et al.  Rational points on elliptic curves , 2006 .

[44]  Mark W. Coffey.  On the coefficients of the Baez-Duarte criterion for the Riemann hypothesis and their extensions , 2006 .

[45]  Craig A. Tracy,et al.  Correlation Functions, Cluster Functions, and Spacing Distributions for Random Matrices , 1998 .

[46]  Вадим Валентинович Зудилин,et al.  Одно из чисел $\zeta(5), \zeta(7), \zeta(9), \zeta(11)$ иррационально@@@One of the numbers $\zeta(5), \zeta(7), \zeta(9), \zeta(11)$ is irrational , 2001 .

[47]  H. Iwaniec,et al.  Analytic Number Theory , 2004 .

[48]  R. A. Raimi.  The First Digit Problem , 1976 .

[49]  Ron Larson,et al.  Elementary Statistics: Picturing the World , 1999 .

[50]  Don Zagier,et al.  Heegner points and derivatives ofL-series , 1986 .

[51]  Helmut Hasse,et al.  Number Theory , 2020, An Introduction to Probabilistic Number Theory.

[52]  Henri Cohen,et al.  Heuristics on class groups of number fields , 1984 .

[53]  Ulrich Derenthal,et al.  On Manin's conjecture for a certain singular cubic surface , 2005, math/0504016.

[54]  W. Rudin.  Principles of mathematical analysis , 1964 .

[55]  Joseph H. Silverman,et al.  A Friendly Introduction to Number Theory , 1996 .

[56]  Steven J. Miller,et al.  The low lying zeros of a GL(4) and a GL(6) family of $L$-functions , 2006 .

[57]  V. Kumar Murty,et al.  Non-vanishing of L-Functions and Applications , 1997 .

[58]  Xian-jin Li,et al.  The Positivity of a Sequence of Numbers and the Riemann Hypothesis , 1997 .

[59]  R. Tennant.  Algebra , 1941, Nature.

[60]  Robert C. Vaughan,et al.  On a variance associated with the distribution of primes in arithmetic progressions , 2001 .

[61]  J. Hoffstein,et al.  An introduction to mathematical cryptography , 2008 .

[62]  S. Lang.  Complex Analysis , 1977 .

[63]  W. Narkiewicz.  The development of prime number theory , 2000 .

[64]  Yakov G. Sinai,et al.  Structure Theorem for (d, g, h)-Maps , 2002 .

[65]  Neal Koblitz,et al.  Why Study Equations over Finite Fields , 1982 .

[66]  Jeffrey C. Lagarias,et al.  Complements to Li's Criterion for the Riemann Hypothesis☆ , 1999 .

[67]  Dennis A. Hejhal,et al.  On the triple correlation of zeros of the zeta function , 1994 .

[68]  Henryk Iwaniec,et al.  Topics in classical automorphic forms , 1997 .

[69]  J. Milne.  Elliptic Curves , 2020 .

[70]  E. Wigner.  Characteristic Vectors of Bordered Matrices with Infinite Dimensions I , 1955 .

[71]  Alfred J. van der Poorten,et al.  Continued Fractions of Algebraic Numbers , 1995 .

[72]  R. Jeffrey.  Formal Logic: Its Scope and Limits , 1981 .

[73]  D. Ridout.  Rational approximations to algebraic numbers , 1957 .

[74]  N. Jacobson,et al.  Basic Algebra II , 1989 .

[75]  J. Coates,et al.  The Conjecture of Birch and Swinnerton-Dyer , 1977, Open Problems in Mathematics.

[76]  J. Brian Conrey,et al.  L-Functions and Random Matrices , 2001 .

[77]  Theodore P. Hill,et al.  The First Digit Phenomenon , 1998, American Scientist.

[78]  T. Apostol.  Introduction to analytic number theory , 1976 .

[79]  K. Mahler.  An introduction to Diophantine Approximation. By J. W. S. Cassbls. Cambridge tracts in mathematics and mathematical physics, No. 45. Pp. 166. 22s. 6d. 1957. (Cambridge) , 1959 .

[80]  K. Mainzer,et al.  Natural Numbers, Integers, and Rational Numbers , 1991 .

[81]  H. Davenport.  On the Distribution of Quadratic Residues (mod p) , 1931 .

[82]  Douglas Quadling,et al.  The Higher Arithmetic , 1954 .

[83]  G. A. Edgar.  Measure, Topology, and Fractal Geometry , 1990 .

[84]  A. Baker.  Transcendental Number Theory , 1975 .

[85]  Henryk Iwaniec,et al.  The Goldbach problem , 2004 .

[86]  J. Wishart.  THE GENERALISED PRODUCT MOMENT DISTRIBUTION IN SAMPLES FROM A NORMAL MULTIVARIATE POPULATION , 1928 .

[87]  A. O. Gelʹfond.  Transcendental and Algebraic Numbers , 1960 .

[88]  C. Luther,et al.  INDEPENDENCE OF THE CONTINUUM HYPOTHESIS , 2009 .

[89]  Giuliana P. Davidoff,et al.  Elementary number theory, group theory, and Ramanujan graphs , 2003 .

[90]  I. Stewart,et al.  Algebraic number theory , 1992, Graduate Studies in Mathematics.

[91]  E. Wigner.  On the Distribution of the Roots of Certain Symmetric Matrices , 1958 .

[92]  P. Shiu.  An introduction to the theory of numbers (5th edition) , by I. Niven, H. S. Zuckerman and H. L. Montgomery. Pp 529. £14·50. 1991. ISBN 0-471-5460031 (Wiley) , 1991 .

[93]  Henri Cohen,et al.  Heuristics on class groups , 1984 .

[94]  Robert M Corless.  Continued fractions and chaos , 1992 .

[95]  A. Granville,et al.  Poisson statistics via the Chinese Remainder Theorem , 2004 .

[96]  F. Reif,et al.  Fundamentals of Statistical and Thermal Physics , 1965 .

[97]  Gerald B. Folland,et al.  Real Analysis: Modern Techniques and Their Applications , 1984 .

[98]  Steven J. Miller,et al.  Order Statistics and Shifted Almost Benford Behavior , 2006 .

[99]  A. Wiles.  Modular Elliptic Curves and Fermat′s Last Theorem(抜粋) (フェルマ-予想がついに解けた!?) , 1995 .

[100]  Gadiel Seroussi,et al.  On hats and other covers , 2002, Proceedings IEEE International Symposium on Information Theory,.

[101]  N. Metropolis.  THE BEGINNING of the MONTE CARLO METHOD , 2022 .

[102]  Michael O. Rubinstein.  A simple heuristic proof of Hardy and Littlewood's conjecture B , 1993 .

[103]  Z. Bai.  METHODOLOGIES IN SPECTRAL ANALYSIS OF LARGE DIMENSIONAL RANDOM MATRICES , A REVIEW , 1999 .

[104]  K. Brown,et al.  Graduate Texts in Mathematics , 1982 .

[105]  Steven J. Miller,et al.  Benford's law, values of L-functions and the 3x+1 problem , 2004, math/0412003.

[106]  Kurt Gödel,et al.  On Formally Undecidable Propositions of Principia Mathematica and Related Systems , 1966 .

[107]  G. Casella,et al.  Statistical Inference , 2003, Encyclopedia of Social Network Analysis and Mining.

[108]  R. Devaney.  An Introduction to Chaotic Dynamical Systems , 1990 .

[109]  E. T..  An Introduction to the Theory of Numbers , 1946, Nature.

[110]  C. Pomerance,et al.  There are infinitely many Carmichael numbers , 1994 .

[111]  N. Koblitz.  Elliptic curve cryptosystems , 1987 .

[112]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[113]  Leo Goldmakher.  On the Limiting Distribution of Eigenvalues of Large Random Regular Graphs with Weighted Edges , 2003 .

[114]  H. Davenport.  Multiplicative Number Theory , 1967 .

[115]  Paul B Garrett.  Making, breaking codes : an introduction to cryptography , 2001 .

[116]  A. Wiles,et al.  Ring-Theoretic Properties of Certain Hecke Algebras , 1995 .

[117]  Mukarram Ahmad,et al.  Continued fractions , 2019, Quadratic Number Theory.

[118]  R. Ayoub.  An Introduction to the Analytic Theory of Numbers , 2006 .

[119]  R. Guy,et al.  The Book of Numbers , 2019, The Crimean Karaim Bible.

[120]  P. Bleher,et al.  The energy level spacing for two harmonic oscillators with generic ratio of frequencies , 1991 .

[121]  Michel Waldschmidt,et al.  On the distribution of solutions of Thue’s equation , 1999 .

[122]  Brendan D. McKay,et al.  The degree sequence of a random graph. I. The models , 1997 .

[123]  B. Mazur,et al.  Rational isogenies of prime degree , 1978 .

[124]  M. Nigrini,et al.  The Use of Benford's Law as an Aid in Analytical Procedures , 1997 .

[125]  Yi-Kai Liu.  Statistical Behavior of the Eigenvalues of Random Matrices , 2001 .

[126]  Richard P. Brent,et al.  A Comparative Study of Algorithms for Computing Continued Fractions of Algebraic Numbers , 1996, ANTS.

[127]  André Voros.  Sharpenings of Li's Criterion for the Riemann Hypothesis , 2006 .

[128]  F. Dyson.  Statistical Theory of the Energy Levels of Complex Systems. I , 1962 .

[129]  P. Levy.  Sur les lois de probabilité dont dépendent les quotients complets et incomplets d'une fraction continue , 1929 .

[130]  N. Miller,et al.  Various Tendencies of Non-Poissonian Distributions Along Subsequences of Certain Transcendental Numbers , 2022 .

[131]  A. Rollett,et al.  The Monte Carlo Method , 2004 .

[132]  S. Skewes,et al.  On the Difference (x)--li(x) (I) , 1933 .

[133]  H. Trotter,et al.  Continued fractions for some algebraic numbers. , 1972 .

[134]  Alexandru Zaharescu,et al.  A metric result on the pair correlation of fractional parts of sequences , 1999 .

[135]  T. D. Browning.  The density of rational points on a certain singular cubic surface , 2004 .

[136]  Arup Bose,et al.  A New Method for Bounding Rates of Convergence of Empirical Spectral Distributions , 2004 .

[137]  D. Champernowne.  The Construction of Decimals Normal in the Scale of Ten , 1933 .

[138]  H. Heilbronn.  On the Average Length of a Class of Finite Continued Fractions , 1969 .

[139]  Barry Mazur,et al.  Modular curves and the eisenstein ideal , 1977 .

[140]  E. Wirsing.  On the theorem of Gauss-Kusmin-Lévy and a Frobenius-type theorem for function spaces , 1974 .

[141]  Jau-Shyong Shiue,et al.  Benford's low for linear recurrence sequences , 1987 .

[142]  Tunc Geveci,et al.  Advanced Calculus , 2014, Nature.

[143]  Giulio Casati,et al.  Statistical properties of the quasi-energy spectrum of a simple integrable system☆ , 1987 .

[144]  C. Porter.  Statistical Theories of Spectra: Fluctuations , 1965 .

[145]  Michael Rosen,et al.  A classical introduction to modern number theory , 1982, Graduate texts in mathematics.

[146]  M. Ram Murty,et al.  Primes in Certain Arithmetic Progressions , 2006 .

[147]  Takeshi Okano.  A Note on the Transcendental Continued Fractions , 1987 .

[148]  Louis de Forcrand,et al.  Higher Arithmetic , 1898, Nature.

[149]  A. Dembo,et al.  Spectral measure of large random Hankel, Markov and Toeplitz matrices , 2003, math/0307330.

[150]  E. Bombieri,et al.  Heights in Diophantine Geometry: Contents , 2006 .

[151]  D. Hilbert,et al.  Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl n ter Potenzen (Waringsches Problem) , 1932 .

[152]  Jeffrey C. Lagarias,et al.  The 3x + 1 Problem and its Generalizations , 1985 .

[153]  R. Adler,et al.  A construction of a normal number for the continued fraction transformation , 1981 .

[154]  E. Wigner,et al.  On the statistical distribution of the widths and spacings of nuclear resonance levels , 1951, Mathematical Proceedings of the Cambridge Philosophical Society.

[155]  Mark J. Nigrini,et al.  Digital analysis and the reduction of auditor litigation risk , 1996 .

[156]  M. Bernhard.  Introduction to Chaotic Dynamical Systems , 1992 .

[157]  Charles M. Grinstead,et al.  Introduction to probability , 1999, Statistics for the Behavioural Sciences.

[158]  W. J. Ellison.  Waring's Problem , 1971 .

[159]  M. Golubitsky,et al.  Stable mappings and their singularities , 1973 .

[160]  N. C. Snaith.  Derivatives of random matrix characteristic polynomials with applications to elliptic curves , 2005 .

[161]  G. Pólya.  Heuristic Reasoning in the Theory of Numbers , 1959 .

[162]  Hugh L. Montgomery,et al.  Beyond pair correlation , 2000 .

[163]  Freeman J. Dyson,et al.  The Threefold Way. Algebraic Structure of Symmetry Groups and Ensembles in Quantum Mechanics , 1962 .

[164]  E. Stein,et al.  Real Analysis: Measure Theory, Integration, and Hilbert Spaces , 2005 .

[165]  K. F. Roth,et al.  Rational approximations to algebraic numbers , 1955 .

[166]  P. J. Forrester,et al.  Developments in random matrix theory , 2003, cond-mat/0303207.

[167]  L. Carleson.  On convergence and growth of partial sums of Fourier series , 1966 .

[168]  Samuel S. Wagstaff,et al.  Sums of Squares of Integers , 2005 .

[169]  I. Vinogradov,et al.  Representation of an odd number as the sum of three primes , 1937 .

[170]  Stefan Rolewicz,et al.  On a problem of moments , 1968 .

[171]  R. D. Richtmyer,et al.  Continued fraction expansions of algebraic numbers , 1962 .

[172]  Michael Rubinstein,et al.  Chebyshev's Bias , 1994, Exp. Math..

[173]  L. Ahlfors.  Complex Analysis , 1979 .

[174]  P. Bickel,et al.  Mathematical Statistics: Basic Ideas and Selected Topics , 1977 .

[175]  Steven J. Miller,et al.  Eigenvalue Spacing Distribution for the Ensemble of Real Symmetric Toeplitz Matrices , 2003 .

[176]  David Pengelley,et al.  Gauss, eisenstein, and the “third” proof of the quadratic reciprocity theorem:ein kleines schauspiel , 1994 .

[177]  L. Olsen,et al.  Extremely non-normal continued fractions , 2003 .

[178]  L. Washington.  Elliptic Curves: Number Theory and Cryptography , 2003 .

[179]  Emmanuel Peyre,et al.  Nombre et répartition de points de hauteur bornée , 2018, Astérisque.

[180]  Peter Sarnak,et al.  Zeros of principal $L$-functions and random matrix theory , 1996 .

[181]  N. J. A. Sloane,et al.  Lexicographic codes: Error-correcting codes from game theory , 1986, IEEE Trans. Inf. Theory.

[182]  Kenneth Falconer,et al.  Fractal Geometry: Mathematical Foundations and Applications , 1990 .

[183]  J. Littlewood,et al.  Some problems of ‘Partitio numerorum’; III: On the expression of a number as a sum of primes , 1923 .

[184]  M. Gaudin.  Sur la loi limite de l'espacement des valeurs propres d'une matrice ale´atoire , 1961 .

[185]  A. J. van der Poorten,et al.  Notes on continued fractions and recurrence sequences , 1991 .

[186]  Michael O. Rubinstein,et al.  Low-lying zeros of L-functions and random matrix theory , 2001 .

[187]  Douglas G. Kelly,et al.  Introduction to Probability , 1993 .

[188]  A. J. van der Poorten.  Fractions of the period of the continued fraction expansion of quadratic integers , 1991, Bulletin of the Australian Mathematical Society.

[189]  R. C. Vaughan,et al.  Sieve Methods, Exponential Sums, and their Applications in Number Theory: On the Montgomery-Hooley Asymptotic Formula , 1997 .

[190]  Leonid A. Bunimovich,et al.  One-dimensional dynamical systems and Benford's law , 2004 .

[191]  Melvyn B. Nathanson,et al.  Additive Number Theory The Classical Bases , 1996 .

[192]  D. Hilbert,et al.  Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl n-ter Potenzen (Waringsches Problem). Dem Andenken an Hermann Minkowski gewidmet. , 1909 .

[193]  Underwood Dudley.  Elementary Number Theory , 1978 .

[194]  Z. Rudnick,et al.  Eigenvalue Spacings for Regular Graphs , 1999 .

[195]  Jens Marklof,et al.  Almost modular functions and the distribution of n2x modulo one , 2003 .

[196]  I. Zakharevich,et al.  A Generalization of Wigner’s Law , 2006 .

[197]  Alberto Candel,et al.  Notes on Fourier Series , 2006 .

[198]  Peter Sarnak,et al.  The distribution of spacings between the fractional parts of n2α , 2001 .

[199]  Dmitry Kleinbock,et al.  Chapter 11 Dynamics of subgroup actions on homogeneous spaces of lie groups and applications to number theory , 2002 .

[200]  Peter Sarnak,et al.  Low lying zeros of families of L-functions , 1999, math/9901141.

[201]  Jeffrey C. Lagarias,et al.  The 3x + 1 Problem: an Annotated Bibliography , 2006 .

[202]  T. Rivoal,et al.  Irrationalité d’une infinité de valeurs de la fonction zêta aux entiers impairs , 2001 .

[203]  Barry Mazur,et al.  Number theory as gadfly , 1991 .

[204]  Steven J. Miller,et al.  Investigations of Zeros near the Central Point of Elliptic Curve L-Functions , 2005, Exp. Math..

[205]  Harold Davenport,et al.  The Higher Arithmetic: An Introduction to the Theory of Numbers , 1952 .

[206]  J. P. Keating,et al.  Integral Moments of L‐Functions , 2002, math/0206018.

[207]  Charles J. Mozzochi.  The Fermat Diary , 2000 .

[208]  Edmund Taylor Whittaker,et al.  A Course of Modern Analysis , 2021 .

[209]  Steven J. Miller.  One- and two-level densities for rational families of elliptic curves: evidence for the underlying group symmetries , 2004, Compositio Mathematica.

[210]  M. L. Mehta,et al.  ON THE STATISTICAL PROPERTIES OF THE LEVEL-SPACINGS IN NUCLEAR SPECTRA , 1960 .

[211]  Dan Boneh,et al.  TWENTY YEARS OF ATTACKS ON THE RSA CRYPTOSYSTEM , 1999 .

[212]  Thomas Koshy,et al.  Fibonacci and Lucas Numbers With Applications , 2018 .

[213]  T. Estermann,et al.  On Goldbach's Problem : Proof that Almost all Even Positive Integers are Sums of Two Primes , 1938 .

[214]  Masayoshi Hata.  Improvement in the irrationality measures of $\pi $ and $\pi ^2 $ , 1992 .

[215]  Hugh L. Montgomery,et al.  Primes in arithmetic progressions. , 1970 .

[216]  Richard P. Brent,et al.  The Distribution of Small Gaps Between Successive Primes , 1974 .

[217]  Jeffrey Shallit,et al.  A Specialised Continued Fraction , 1993, Canadian Journal of Mathematics.

[218]  André Weil,et al.  Prehistory of the Zeta-Function , 1989 .

[219]  J. E. Nymann.  An Application of Diophantine Approximation , 1969 .

[220]  H. Weyl.  The Classical Groups , 1940 .

[221]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[222]  P. Billingsley,et al.  Probability and Measure , 1980 .

[223]  Richard P. Brent,et al.  Irregularities in the distribution of primes and twin primes , 1975 .

[224]  Brendan D. McKay,et al.  The degree sequence of a random graph. I. The models , 1997, Random Struct. Algorithms.

[225]  Peter Szüsz.  On the length of continued fractions representing a rational number with given denominator , 1980 .

[226]  B. McKay.  The expected eigenvalue distribution of a large regular graph , 1981 .

[227]  S. Lang,et al.  Introduction to Diophantine Approximations , 1995 .

[228]  Donald E. Knuth,et al.  The art of computer programming. Vol.2: Seminumerical algorithms , 1981 .

[229]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[230]  J. Neukirch.  Algebraic Number Theory , 1999 .

[231]  Steven J. Miller,et al.  Introduction to: 1- and 2-Level Densities for Families of Elliptic Curves: Evidence for the Underlying Group Symmetries , 2003 .

[232]  Audra E. Kosh,et al.  Linear Algebra and its Applications , 1992 .

[233]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[234]  Anne Boutet de Monvel,et al.  Some Elementary Results around the Wigner Semicircle Law , 2001 .

[235]  John von Neumann,et al.  Continued fraction expansion of 2^{1/3} , 1955 .

[236]  D. R. Heath-Brown,et al.  The Theory of the Riemann Zeta-Function , 1987 .

[237]  P. A. Mello,et al.  Random matrix physics: Spectrum and strength fluctuations , 1981 .

[238]  K. Williams,et al.  Gauss and Jacobi sums , 2021, Mathematical Surveys and Monographs.

[239]  T. Hill.  A Statistical Derivation of the Significant-Digit Law , 1995 .

[240]  Daniel Nahum Rockmore.  Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers , 2005 .

[241]  Peter Sarnak,et al.  Dirichlet L-functions at the central point , 1999 .

[242]  Elias M. Stein,et al.  Fourier Analysis: An Introduction , 2003 .

[243]  N. J. A. Sloane,et al.  The On-Line Encyclopedia of Integer Sequences , 2003, Electron. J. Comb..

[244]  A. Odlyzko.  On the distribution of spacings between zeros of the zeta function , 1987 .

[245]  D. R. Heath-Brown.  The density of rational points on Cayley's cubic surface , 2002, math/0210333.

[246]  Herbert S. Wilf,et al.  Algorithms and Complexity , 1994, Lecture Notes in Computer Science.

[247]  Mark W. Coffey.  Toward Verification of the Riemann Hypothesis: Application of the Li Criterion , 2005 .

[248]  Ronald L. Graham,et al.  Concrete mathematics - a foundation for computer science , 1991 .

[249]  P. Bleher,et al.  The energy level spacing for two harmonic oscillators with golden mean ratio of frequencies , 1990 .

[250]  Xavier.  The 10 13 first zeros of the Riemann Zeta function , and zeros computation at very large height , 2004 .

[251]  Steven J. Miller,et al.  Distribution of Eigenvalues for the Ensemble of Real Symmetric Toeplitz Matrices , 2005 .

[252]  P. Borwein,et al.  The Riemann Hypothesis , 2008 .

[253]  Martin Aigner,et al.  Proofs from THE BOOK , 1998 .

[254]  J. Borwein,et al.  Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity , 1998 .

[255]  E. Stein,et al.  Complex Analysis , 2003 .

[256]  G. H. Hardy,et al.  Some problems of ‘Partitio numerorum’ (VI): Further researches in Waring's Problem , 1925 .

[257]  Victor S. Miller,et al.  Use of Elliptic Curves in Cryptography , 1985, CRYPTO.

[258]  M. Ram Murty,et al.  Problems in analytic number theory , 2000 .

[259]  Loo Keng Hua,et al.  Introduction to number theory , 1982 .

[260]  J. Shohat,et al.  The problem of moments , 1943 .

[261]  Neal Koblitz,et al.  A Survey of Number Theory and Cryptography , 2000 .

[262]  C. P. Hughes,et al.  Mock-Gaussian behaviour for linear statistics of classical compact groups , 2002 .

[263]  te Herman Riele,et al.  On the Sign of the Difference ir( x) — li( x) , 2010 .

[264]  A. Weil.  Numbers of solutions of equations in finite fields , 1949 .

[265]  B. Mandelbrot.  Fractal Geometry of Nature , 1984 .

[266]  C. J. Mozzochi,et al.  Siegel zeros and the Goldbach problem , 1983 .

[267]  Peter Sarnak,et al.  The non-vanishing of central values of automorphic L-functions and Landau-Siegel zeros , 2000 .

[268]  Karl R. Stromberg.  The Banach-Tarski Paradox , 1979 .