Expanding polynomials over finite fields of large characteristic, and a regularity lemma for definable sets
暂无分享,去创建一个
[1] Michele de Franchis,et al. Un teorema sulle involuzioni irrazionali , 1913 .
[2] A. Pillay,et al. Definable subgroups of algebraic groups over finite fields. , 1995 .
[3] Donal O'Shea,et al. Ideals, varieties, and algorithms - an introduction to computational algebraic geometry and commutative algebra (2. ed.) , 1997, Undergraduate texts in mathematics.
[4] Lajos Rónyai,et al. A Combinatorial Problem on Polynomials and Rational Functions , 2000, J. Comb. Theory, Ser. A.
[5] I. Shkredov,et al. On monochromatic solutions of some nonlinear equations in ℤ/pℤ , 2009, 0909.3269.
[6] V. Zoonekynd. Théorème de Van Kampen pour les champs algébriques , 2001 .
[7] A. Weil. Numbers of solutions of equations in finite fields , 1949 .
[8] Norbert Hegyv'ari,et al. Explicit constructions of extractors and expanders , 2012, 1206.1146.
[9] A. Macintyre,et al. Definable sets over finite fields. , 1992 .
[10] Vojtech Rödl,et al. The Uniformity Lemma for hypergraphs , 1992, Graphs Comb..
[11] Jean-Pierre Serre,et al. Exemples de variétés projectives conjuguées non homéomorphes , 2003 .
[12] S. Shelah,et al. Regularity lemmas for stable graphs , 2011, 1102.3904.
[13] Emmanuel Kowalski. Exponential sums over definable subsets of finite fields , 2005 .
[14] Jacob T. Schwartz,et al. Fast Probabilistic Algorithms for Verification of Polynomial Identities , 1980, J. ACM.
[15] György Elekes,et al. How to find groups? (and how to use them in Erdős geometry?) , 2012, Comb..
[16] K. Conrad,et al. Finite Fields , 2018, Series and Products in the Development of Mathematics.
[17] J. Bourgain,et al. MORE ON THE SUM-PRODUCT PHENOMENON IN PRIME FIELDS AND ITS APPLICATIONS , 2005 .
[18] John Lenz,et al. The poset of hypergraph quasirandomness , 2012, Random Struct. Algorithms.
[19] Katalin Gyarmati,et al. Equations in finite fields with restricted solution sets. I (Character sums) , 2008 .
[20] D. Mumford. The red book of varieties and schemes , 1988 .
[21] Gnter Tamme,et al. Teilkörper höheren Geschlechts eines algebraischen Funktionenkörpers , 1972 .
[22] Joe W. Harris,et al. Algebraic Geometry: A First Course , 1995 .
[23] I. Shafarevich. Basic algebraic geometry , 1974 .
[24] P. Deligne,et al. Groupes de monodromie en geometrie algebrique , 1972 .
[25] Vojtech Rödl,et al. Regular Partitions of Hypergraphs: Regularity Lemmas , 2007, Combinatorics, Probability and Computing.
[26] Ben Green,et al. Approximate Subgroups of Linear Groups , 2010, 1005.1881.
[27] Chun-Yen Shen,et al. Fourier analysis and expanding phenomena in finite fields , 2009, 0909.5471.
[28] Vojtech Rödl,et al. Regularity Lemma for k‐uniform hypergraphs , 2004, Random Struct. Algorithms.
[29] Misha Rudnev,et al. Erdös distance problem in vector spaces over finite fields , 2005 .
[30] W. T. Gowers,et al. Hypergraph regularity and the multidimensional Szemerédi theorem , 2007, 0710.3032.
[31] Fan Chung Graham,et al. Regularity Lemmas for Hypergraphs and Quasi-randomness , 1991, Random Struct. Algorithms.
[32] Alexander Grothendieck,et al. Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux (SGA 2) , 1962 .
[33] K. Gödel. The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis. , 1938, Proceedings of the National Academy of Sciences of the United States of America.
[34] W. T. Gowers,et al. Lower bounds of tower type for Szemerédi's uniformity lemma , 1997 .
[35] Joe W. Harris,et al. Principles of Algebraic Geometry , 1978 .
[36] Michael D. Fried,et al. Solving Diophantine Problems Over All Residue Class Fields of a Number Field and All Finite Fields , 1976 .
[37] Richard J. Lipton,et al. A Probabilistic Remark on Algebraic Program Testing , 1978, Inf. Process. Lett..
[38] B. M. Fulk. MATH , 1992 .
[39] Katalin Gyarmati,et al. Equations in finite fields with restricted solution sets. II (Algebraic equations) , 2008 .
[40] Ehud Hrushovski,et al. Stable group theory and approximate subgroups , 2009, 0909.2190.
[41] József Solymos,et al. Incidences and the spectra of graphs , 2008 .
[42] Terence Tao. A variant of the hypergraph removal lemma , 2006, J. Comb. Theory, Ser. A.
[43] C. Wampler,et al. Basic Algebraic Geometry , 2005 .
[44] Catarina I. Kiefe. Sets definable over finite fields: their zeta-functions , 1976 .
[45] C. Torrance. Review: Kurt Gödel, The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis with the Axioms of Set Theory , 1941 .
[46] Doowon Koh,et al. Generalized incidence theorems, homogeneous forms and sum-product estimates in finite fields , 2008, European journal of combinatorics (Print).
[47] Ben Green,et al. The structure of approximate groups , 2011, Publications mathématiques de l'IHÉS.
[48] Joseph L. Taylor. Several Complex Variables with Connections to Algebraic Geometry and Lie Groups , 2002 .
[49] Moshe Jarden,et al. THE ELEMENTARY THEORY OF FINITE FIELDS , 2004 .
[50] Sergei Konyagin,et al. Distance sets of well-distributed planar sets for polygonal norms , 2004 .
[51] W. T. Gowers,et al. A New Proof of Szemerédi's Theorem for Arithmetic Progressions of Length Four , 1998 .
[52] S. Lang,et al. NUMBER OF POINTS OF VARIETIES IN FINITE FIELDS. , 1954 .
[53] T. Willmore. Algebraic Geometry , 1973, Nature.
[54] Boris Bukh. Sums of Dilates , 2008, Comb. Probab. Comput..
[55] Jacob Tsimerman,et al. Sum–product estimates for rational functions , 2010, 1002.2554.
[56] Lou van den Dries,et al. Decidability and undecidability theorems for PAC-fields , 1981 .
[57] RodlVojtech,et al. Regular Partitions of Hypergraphs , 2007 .
[58] Jozsef Solymosi,et al. Expanding Polynomials over the rationals , 2012, 1212.3365.
[59] S. Kleiman. Bertini and his two fundamental theorems , 1997, alg-geom/9704018.
[60] Richard Zippel,et al. Probabilistic algorithms for sparse polynomials , 1979, EUROSAM.
[61] W. T. Gowers,et al. A NEW PROOF OF SZEMER ´ EDI'S THEOREM , 2001 .
[62] Alexander Grothendieck,et al. Éléments de géométrie algébrique (rédigés avec la collaboration de Jean Dieudonné) : III. Étude cohomologique des faisceaux cohérents, Première partie , 1961 .
[63] R. Ho. Algebraic Topology , 2022 .
[64] Daqing Wan,et al. Generators and irreducible polynomials over finite fields , 1997, Math. Comput..
[65] Илья Дмитриевич Шкредов,et al. О монохроматических решениях некоторых нелинейных уравнений в $\mathbb Z/p\mathbb Z$@@@On Monochromatic Solutions of Some Nonlinear Equations in $\mathbb Z/p\mathbb Z$ , 2010 .
[66] Toni Robertson,et al. Building bridges: negotiating the gap between work practice and technology design , 2000, Int. J. Hum. Comput. Stud..
[67] Chun-Yen Shen,et al. On the size of the set A(A + 1) , 2008, 0811.4206.
[68] Ralf Fröberg,et al. An introduction to Gröbner bases , 1997, Pure and applied mathematics.
[69] Michael E. Zieve,et al. ON RITT'S POLYNOMIAL DECOMPOSITION THEOREMS , 2008, 0807.3578.
[70] Derrick Hart,et al. Sums and products in finite fields: an integral geometric viewpoint , 2007, 0705.4256.
[71] Van H. Vu,et al. SUM-PRODUCT ESTIMATES VIA DIRECTED EXPANDERS , 2008 .
[72] A. Schinzel. Polynomials with Special Regard to Reducibility: Polynomials over a number field , 2000 .
[73] H. DAVENPORT. Two Problems Concerning Polynomials. , 1964 .
[74] Leila Schneps,et al. Galois groups and fundamental groups , 2003 .
[75] Alain Plagne,et al. Sums of Dilates in Groups of Prime Order , 2011, Combinatorics, Probability and Computing.
[76] David Schwein,et al. Étale Cohomology , 2018, Translations of Mathematical Monographs.
[77] E. Szemerédi. Regular Partitions of Graphs , 1975 .
[78] Fan Chung Graham,et al. Quasi-Random Hypergraphs , 1990, Random Struct. Algorithms.
[79] M. A. Clements. Terence Tao , 1984 .
[80] Terence Tao,et al. The Kakeya set and maximal conjectures for algebraic varieties over finite fields , 2009, 0903.1879.
[81] Timothy S. Murphy,et al. Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals , 1993 .