C. Pomerance

发表

On a problem of Oppenheim concerning “factorisatio numerorum”

P. Erdös, E. R. Canfield, C. Pomerance, 1983 .

On the number of false witnesses for a composite number

P. Erdös, C. Pomerance, 1986 .

A rigorous time bound for factoring integers

H. Lenstra, C. Pomerance, 1992 .

On distinguishing prime numbers from composite numbers

L. Adleman, C. Pomerance, R. Rumely, 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

The probability that a random probable prime is composite

C. Pomerance, Su Hee Kim, 1989 .

There are infinitely many Carmichael numbers

C. Pomerance, W. Alford, Andrew Granville, 1994 .

Factoring integers with the number field sieve

H. Lenstra, C. Pomerance, J. Buhler, 1993 .

Average case error estimates for the strong probable prime test

I. Damgård, C. Pomerance, P. Landrock, 1993 .

Prime Numbers: A Computational Perspective

C. Pomerance, R. Crandall, 2002 .

Fast, Rigorous Factorization and Discrete Logarithm Algorithms

C. Pomerance, 1987 .

On the distribution of pseudoprimes

C. Pomerance, 1981 .

Rigorous discrete logarithm computations in finite fields via smooth polynomials

C. Pomerance, R. L. Bender, 1997 .

A hyperelliptic smoothness test. I

C. Pomerance, H. Lenstra, Jr., J. Pila, 1993, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

The Quadratic Sieve Factoring Algorithm

Carl Pomerance, C. Pomerance, 1985, EUROCRYPT.

ON THE PROBLEM OF UNIQUENESS FOR THE MAXIMUM STIRLING NUMBER(S) OF THE SECOND KIND

E. R. Canfield, C. Pomerance, E. Canfield, 2001 .

Elementary thoughts on discrete logarithms

C. Pomerance, 2008 .

On the normal number of prime factors of $\phi(n)$

P. Erdös, C. Pomerance, 1985 .

Unusually large gaps between consecutive primes

C. Pomerance, H. Maier, 1990 .

Carmichael's lambda function

P. Erdos, C. Pomerance, E. Schmutz, 1991 .

Explicit estimates for the distribution of numbers free of large prime factors

Jared D. Lichtman, C. Pomerance, J. Lichtman, 2017, 1705.02442.

The distribution of Lucas and elliptic pseudoprimes

C. Pomerance, D. M. Gordon, 1991 .

Algorithms for the Multiplication Table Problem

R. Brent, C. Pomerance, David Purdum, 2019, 1908.04251.

Very short primality proofs

C. Pomerance, 1987 .

Recent developments in primality testing

C. Pomerance, 1981 .

On the largest prime factors ofn andn + 1

P. Erdös, C. Pomerance, 1978 .

Fibonacci Integers

Stephan G. Wagner, C. Pomerance, 2010 .

On the largest prime factor of a Mersenne number

C. Pomerance, L. Murata, 2004 .

On primitive divisors of Mersenne numbers

C. Pomerance, 1986 .

THE RISE OF STATISTICAL THINKING

C. Pomerance, T. Porter, CARL POMERANCE, 2013 .

Combinatorial number theory

András Sárközy, Carl Pomerance, C. Pomerance, 1996 .

Rigorous, subexponential algorithms for discrete logarithms over finite fields

Carl Pomerance, C. Pomerance, Renet Lovorn, 1992 .

The Role of Smooth Numbers in Number Theoretic Algorithms

Carl Pomerance, C. Pomerance, 1995 .

On a conjecture of Crandall concerning the qx + 1 problem

Carl Pomerance, C. Pomerance, Z. Franco, 1995 .

Smooth numbers and the quadratic sieve

Carl Pomerance, C. Pomerance, 2008 .

Counting elliptic curves with an isogeny of degree three

C. Pomerance, J. Voight, Maggie Pizzo, 2019, Proceedings of the American Mathematical Society, Series B.

ON CARMICHAEL NUMBERS IN ARITHMETIC PROGRESSIONS

C. Pomerance, W. Banks, 2010, Journal of the Australian Mathematical Society.

PRIMALITY TESTING: VARIATIONS ON A THEME OF LUCAS

C. Pomerance, 2022 .

On the Distribution in Residue Classes of Integers with a Fixed Sum of Digits

C. Pomerance, C. Mauduit, A. Sárközy, 2005 .

#A82 INTEGERS 18 (2018) DENSITY OF SINGULAR PAIRS OF INTEGERS

C. Pomerance, R. Nedela, 2018 .

On Primes Recognizable in Deterministic Polynomial Time

Carl Pomerance, Sergei Konyagin, C. Pomerance, 2013, The Mathematics of Paul Erdős I.

Some problems of Erdős on the sum-of-divisors function

C. Pomerance, P. Pollack, 2016 .

Sierpinski and Carmichael numbers

Carrie E. Finch, C. Pomerance, F. Luca, 2014 .

Small Sets Satisfying the Central Sets Theorem

J. Nesetril, R. Nowakowski, C. Pomerance, 2009 .

Timed Fair Exchange of Standard Signatures

Juan A. Garay, Carl Pomerance, J. Garay, 2003, IACR Cryptology ePrint Archive.

The arithmetic mean of the divisors of an integer

P. Erdös, P. Bateman, E. Straus, 1981 .

Convergence Rates for Runlength Constrained Capacities

K. Zeger, C. Pomerance, 2001 .

On the number of distinct values of Euler's φ-function

C. Pomerance, H. Maier, 1988 .

Advances in Cryptology — CRYPTO ’87

Carl Pomerance, C. Pomerance, 2000, Lecture Notes in Computer Science.

COUNTING INTEGERS WITH A SMOOTH TOTIENT

C. Pomerance, W. Banks, I. Shparlinski, 2018, The Quarterly Journal of Mathematics.

On the counting function of irregular primes

C. Pomerance, F. Luca, Amalia Pizarro-Madariaga, 2015 .

ON UNTOUCHABLE NUMBERS AND RELATED PROBLEMS

C. Pomerance, Hee-Sung Yang, 2012 .

On the periods of the linear congruential and power generators

C. Pomerance, P. Kurlberg, 2004, math/0405120.

On the Critical Exponent for k-Primitive Sets

Jared D. Lichtman, C. Pomerance, T. Chan, 2020, Combinatorica.

AN ANALOGUE OF GRLMM ' S PROBLEM OF FINDING DISTINCT PRIME FACTORS OF CONSECUTIVE INTEGERS

C. Pomerance, Paul ErdZs, 1983 .

A Search for Elliptic Curves With Large Rank

C. Pomerance, D. E. Penney, 1974 .

Finding the group structure of elliptic curves over finite fields

C. Pomerance, I. Shparlinski, J. Friedlander, 2005, Bulletin of the Australian Mathematical Society.

On the Distribution of Pseudopowers

C. Pomerance, I. Shparlinski, S. Konyagin, 2007, Canadian Journal of Mathematics.

Residue classes free of values of Euler's function

C. Pomerance, S. Konyagin, Kevin Ford, 2020, 2005.01078.

INTEGERS 9 Supplement ( 2009 ) ON PSEUDOSQUARES AND PSEUDOPOWERS

C. Pomerance, I. Shparlinski, 2009 .

On Pseudosquares and Pseudopowers

C. Pomerance, I. Shparlinski, 2007, 0712.1081.

LOWER BOUNDS ON THE PERIOD OF SOME PSEUDORANDOM NUMBER GENERATORS PÄR KURLBERG AND CARL POMERANCE

C. Pomerance, P. Kurlberg, 2007 .

The iterated Carmichael \lambda-function and the number of cycles of the power generator

C. Pomerance, G. Martin, 2004, math/0406335.

On generalizing Artins conjecture on primitive roots to composite moduli

C. Pomerance, Shuguang Li, 2003 .

On integers which are the sum of a power of 2 and a polynomial value

C. Pomerance, C. Moreira, F. Luca, 2014 .

Long gaps in sieved sets

T. Tao, C. Pomerance, S. Konyagin, 2018, Journal of the European Mathematical Society.

The pseudoprimes to 25⋅10⁹

Carl Pomerance, Samuel S. Wagstaff, J. L. Selfridge, 1980 .

POPULAR VALUES OF EULER'S FUNCTION

Carl Pomerance, C. Pomerance, 1980 .

On Carmichael’s conjecture

C. Pomerance, 1974 .

The aliquot constant, after Bosma and Kane

C. Pomerance, 2018 .

THE FIRST FUNCTION AND ITS ITERATES

C. Pomerance, 2016 .

Three elliptic curves with rank at least seven

C. Pomerance, D. E. Penney, 1975 .

INTEGERS 22 (2022) COPRIME MATCHINGS

C. Pomerance, 2022 .

INTEGERS 22 (2022) COPRIME PERMUTATIONS

C. Pomerance, 2022 .

The prime number graph

C. Pomerance, 1979 .

Error estimates for the Davenport-Heilbronn theorems

C. Pomerance, K. Belabas, M. Bhargava, 2010 .

The denominators of the Bernoulli numbers

Carl Pomerance, Samuel S. Wagstaff, S. Wagstaff, 2021, Acta Arithmetica.

Some thoughts on pseudoprimes

Carl Pomerance, Samuel S. Wagstaff, S. Wagstaff, 2021, 2103.00679.

Sets of monotonicity for Euler’s totient function

C. Pomerance, P. Pollack, Enrique Treviño, 2012, The Ramanujan Journal.

Automaticity II: Descriptional Complexity in the Unary Case

Jeffrey Shallit, John Michael Robson, Carl Pomerance, 1997, Theor. Comput. Sci..

The Briscoe Center for American History

C. Pomerance, 1975 .

The distribution of smooth numbers in arithmetic progressions

Antal Balog, Carl Pomerance, C. Pomerance, 1992 .

On the asymptotic effectiveness of Weil descent attacks

Igor E. Shparlinski, Alfred Menezes, Carl Pomerance, 2010, J. Math. Cryptol..

A search for Wieferich and Wilson primes

Karl Dilcher, Richard E. Crandall, Carl Pomerance, 1997, Math. Comput..

New Ideas for Factoring Large Integers

Jeffrey W. Smith, Carl Pomerance, Samuel S. Wagstaff, 1983, CRYPTO.

Number Theory

Jeffrey Shallit, Carl Pomerance, Jon Grantham, 1999, Handbook of Discrete and Combinatorial Mathematics.

SOME NEW RESULTS ON ODD PERFECT NUMBERS

C. Pomerance, J. Hunsucker, G. G. Dandapat, 1975 .

On multiply perfect numbers with a special property.

Carl Pomerance, C. Pomerance, 1975 .

The Search for Prime Numbers.

Carl Pomerance, C. Pomerance, 1982 .

The Development of the Number Field Sieve

Carl Pomerance, Arthur Y. Hung, C. Pomerance, 1994 .

A Pipeline Architecture for Factoring Large Integers with the Quadratic Sieve Algorithm

Jeffrey W. Smith, Carl Pomerance, J. W. Smith, 1988, SIAM J. Comput..

On numbers n dividing the nth term of a linear recurrence

C. Pomerance, F. Luca, I. Shparlinski, 2010, Proceedings of the Edinburgh Mathematical Society.

The Mathematics of Paul Erdős I

László Babai, Carl Pomerance, L. Babai, 2013 .

On the average number of groups of square-free order

C. Pomerance, 1987 .

Lecture Notes on Primality Testing and Factoring: A Short Course at Kent State University

Carl Pomerance, C. Pomerance, 1984 .

Coprime permutations

C. Pomerance, 2022, 2203.03085.

On the distribution of sociable numbers

Paul Pollack, Carl Pomerance, C. Pomerance, 2009 .

Proof of D. J. Newman's coprime mapping conjecture

Carl Pomerance, J. L. Selfridge, C. Pomerance, 1980 .

Prime Numbers: A Computational Perspective

C. Pomerance, R. Crandall, 2002 .

Squarefree smooth numbers and Euclidean prime generators

C. Pomerance, A. Booker, 2016, 1607.01557.

Generating random factored Gaussian integers, easily

Noah Lebowitz-Lockard, Carl Pomerance, C. Pomerance, 2015, Math. Comput..

Fixed Points for Discrete Logarithms

Carl Pomerance, K. Soundararajan, Mariana Levin, 2010, ANTS.

On the binary expansions of algebraic numbers

J. Borwein, C. Pomerance, R. Crandall, 2003 .

Smooth Orders and Cryptographic Applications

Igor E. Shparlinski, Carl Pomerance, C. Pomerance, 2002, ANTS.

PRIMALITY TESTING: VARIATIONS ON A THEME OF LUCAS

C. Pomerance, 2022 .

On integers which are the sum of a power of 2 and a polynomial value

C. Pomerance, C. Moreira, F. Luca, 2014, Bulletin of the Brazilian Mathematical Society, New Series.

The expected number of random elements to generate a finite abelian group

Carl Pomerance, C. Pomerance, 2002, Period. Math. Hung..

On the number of divisors of n

P. Erdös, C. Pomerance, A. Ivic, 1996 .

Elliptic curves with Galois-stable cyclic subgroups of order 4

Edward F. Schaefer, C. Pomerance, 2020, Research in Number Theory.

The generation of random numbers that are probably prime

Gilles Brassard, Claude Crépeau, Carl Pomerance, 1988, Journal of Cryptology.

A Hyperelliptic Smoothness Test, II

Carl Pomerance, H. Lenstra, C. Pomerance, 2002 .

View-Obstruction Problems, III

Carl Pomerance, C. Pomerance, T. Cusick, 1984 .

The Maximal Density of Product-Free Sets in ℤ/nℤ

J. Lagarias, C. Pomerance, P. Kurlberg, 2011, 1111.2634.

Counterexamples to the modified Weyl–Berry conjecture on fractal drums

Michel L. Lapidus, Carl Pomerance, C. Pomerance, 1996, Mathematical Proceedings of the Cambridge Philosophical Society.

The Riemann Zeta-Function and the One-Dimensional Weyl-Berry Conjecture for Fractal Drums

Michel L. Lapidus, Carl Pomerance, C. Pomerance, 1993 .

On Sets of Integers Which Are Both Sum-Free and Product-Free

Jeffrey C. Lagarias, Carl Pomerance, Par Kurlberg, 2012, Integers.

The Artin-Carmichael primitive root problem on average

C. Pomerance, Shuguang Li, 2009 .

Remarks on the Pólya–Vinogradov Inequality

Carl Pomerance, C. Pomerance, 2011, Integers.

On the smallest pseudopower

Igor E. Shparlinski, Carl Pomerance, Jean Bourgain, 2009 .

On the largest prime factors ofn andn + 1

P. Erdös, C. Pomerance, 1978 .

Multiplicative Structure of Values of the Euler Function

Igor E. Shparlinski, Carl Pomerance, William D. Banks, 2004 .

Counting the Integers Factorable via Cyclotomic Methods

Jonathan P. Sorenson, Carl Pomerance, J. Sorenson, 1995, J. Algorithms.

A Tale of Two Sieves

Carl Pomerance, Paul Erdös, P. Erdös, 1998 .

Reduction of Huge, Sparse Matrices over Finite Fields Via Created Catastrophes

Jeffrey W. Smith, Carl Pomerance, Jeffrey W. Smith, 1992, Exp. Math..

Eigenvalues of the Laplacian on domains with fractal boundary

C. Pomerance, P. Pollack, 2019, Horizons of Fractal Geometry and Complex Dimensions.

The reciprocal sum of the amicable numbers

Carl Pomerance, My Hanh Nguyen, C. Pomerance, 2018, Math. Comput..

On the proportion of numbers coprime to a given integer

P. Erdos, C. Pomerance, F. Luca, 2008 .

On composite n for which φ(n) n -1

C. Pomerance, 1977 .

SETS WITH PRESCRIBED ARITHMETIC DENSITIES

C. Pomerance, F. Luca, 2008 .

A new lower bound for the pseudoprime counting function

Carl Pomerance, C. Pomerance, 1982 .

On a problem of Arnold: The average multiplicative order of a given integer

C. Pomerance, P. Kurlberg, 2011, 1108.5209.

The range of the sum-of-proper-divisors function

C. Pomerance, F. Luca, 2015 .

Paul Erdős and the Rise of Statistical Thinking in Elementary Number Theory

C. Pomerance, P. Pollack, 2013 .

On the Normal Behavior of the Iterates Of some Arithmetic Functions

Paul Erdös, Carl Pomerance, P. Erdös, 1990 .

On the distribution of amicable numbers.

Carl Pomerance, C. Pomerance, 1977 .

On the distribution of amicable numbers. II.

Carl Pomerance, C. Pomerance, 1977 .

On a nonintegrality conjecture

Florian Luca, Carl Pomerance, C. Pomerance, 2021, European Journal of Mathematics.

Progress towards a nonintegrality conjecture

C. Pomerance, Daniel López-Aguayo, Thotsaphon Thongjunthug, 2019, European Journal of Mathematics.

Cyclotomic Coincidences

C. Pomerance, Simon Rubinstein-Salzedo, 2019, Exp. Math..

A note on the least prime in an arithmetic progression

C. Pomerance, 1980 .

Progress towards a nonintegrality conjecture

C. Pomerance, Daniel López-Aguayo, Thotsaphon Thongjunthug, 2019, European Journal of Mathematics.

On the least prime incertain arithmetic

C. Pomerance, progressionsbyAndrew Granville, 2008 .

Maximal height of divisors of $x\sp n-1$

Nathan C. Ryan, C. Pomerance, 2007 .

Cryptology and Computational Number Theory

Jeffrey C. Lagarias, Shafi Goldwasser, Arjen K. Lenstra, 1997 .

Journal de Théorie des Nombres de Bordeaux 00 ( XXXX ) , 000 – 000 On the binary expansions of algebraic numbers par

J. Borwein, C. Pomerance, R. Crandall, 2003 .

Common values of the arithmetic functions ϕ and σ

Florian Luca, Kevin Ford, Carl Pomerance, 2009, 0906.3380.

Maier Matrices Beyond Z

J. Nesetril, R. Nowakowski, C. Pomerance, 2009 .