## Pomerance, Carl Bernard

Compute Distance To:
 Author ID: pomerance.carl Published as: Pomerance, Carl; Pomerance, C.; Pomerance, Carl Bernard; Pomerance, Carl B. more...less Homepage: https://www.math.dartmouth.edu/~carlp/ External Links: MGP · ORCID · Wikidata · Google Scholar · ResearchGate · Math-Net.Ru · dblp · GND · IdRef
 Documents Indexed: 240 Publications since 1974, including 3 Books 11 Contributions as Editor · 1 Further Contribution Biographic References: 2 Publications Co-Authors: 142 Co-Authors with 196 Joint Publications 4,740 Co-Co-Authors
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### Co-Authors

 54 single-authored 25 Luca, Florian 21 Erdős, Pál 14 Pollack, Paul 14 Shparlinski, Igor E. 11 Sárközy, András 8 Nešetřil, Jaroslav 7 Nathanson, Melvyn Bernard 6 Banks, William D. 6 Ford, Kevin B. 6 Granville, Andrew James 6 Konyagin, Sergeĭ Vladimirovich 5 Friedlander, John Benjamin 5 Kurlberg, Pär 5 Landman, Bruce M. 5 Lenstra, Hendrik W. jun. 5 Lichtman, Jared Duker 4 Crandall, Richard E. 4 Ivić, Aleksandar 4 Lagarias, Jeffrey C. 4 Li, Shuguang 4 Nowakowski, Richard Joseph 4 Penney, David E. 4 Wagstaff, Samuel Standfield jun. 3 Alford, William Robert 3 Bateman, Paul Trevier 3 Buhler, Joe P. 3 Canfield, E. Rodney 3 Hunsucker, John L. 3 Lapidus, Michel L. 3 Maier, Helmut 3 Martin, Greg 3 Selfridge, John L. 2 Diamond, Harold George 2 Gordon, Daniel M. 2 Graham, Sidney W. 2 Kobayashi, Mitsuo 2 Mauduit, Christian 2 Pila, Jonathan 2 Robertson, Aaron 2 Shallit, Jeffrey O. 2 Stewart, Cameron L. 2 Tenenbaum, Gérald 2 Thompson, Lola 2 Weingartner, Andreas J. 1 Adleman, Leonard Max 1 Alba González, Juan José 1 Alon, Noga M. 1 Anavi, Aria 1 Babai, László 1 Bailey, David Harold 1 Balazard, Michel 1 Balog, Antal 1 Beauchemin, Pierre 1 Belabas, Karim 1 Bender, Renet Lovorn 1 Bhargava, Manjul 1 Booker, Andrew R. 1 Borwein, Jonathan Michael 1 Bourgain, Jean 1 Brassard, Gilles 1 Brent, Richard Peirce 1 Butler, Steven Kay 1 Chan, Tsz Ho 1 Cheng, Fred Yuanyou 1 Chow, Sam 1 Chung, Fan 1 Crépeau, Claude 1 Cusick, Thomas W. 1 Damgård, Ivan Bjerre 1 Dandapat, G. G. 1 de la Bretèche, Régis 1 Dence, Thomas P. 1 Deshouillers, Jean-Marc 1 Diaconis, Persi Warren 1 Dilcher, Karl 1 Ekstrom, Aaron 1 Filaseta, Michael A. 1 Finch, Carrie E. 1 Fletcher, Peter 1 Franco, Zachary M. 1 Freiberg, Tristan 1 Gagola, Stephen Michael jun. 1 Garay, Juan A. 1 Garfunkel, Solomon A. 1 Goutier, Claude 1 Gowers, Tim 1 Graham, Ronald Lewis 1 Holt, Jeffrey J. 1 Hu, Yilan 1 Hurlbert, Glenn H. 1 Karabina, Koray 1 Kim, Su Hee 1 Kinlaw, Paul A. 1 Kiss, Péter 1 Kleitman, Daniel J. 1 Knuth, Donald Ervin 1 Kozek, Mark 1 Lacampagne, Carole B. 1 Laishram, Shanta 1 Landrock, Peter ...and 58 more Co-Authors
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### Serials

 21 Mathematics of Computation 17 Acta Arithmetica 16 Integers 11 Journal of Number Theory 7 The Ramanujan Journal 6 Proceedings of the American Mathematical Society 5 Mathematika 4 Colloquium Mathematicum 4 Publicationes Mathematicae Debrecen 4 International Journal of Number Theory 3 American Mathematical Monthly 3 Illinois Journal of Mathematics 3 Journal für die Reine und Angewandte Mathematik 3 Pacific Journal of Mathematics 3 Notices of the American Mathematical Society 2 Rocky Mountain Journal of Mathematics 2 Bulletin of the London Mathematical Society 2 Indian Journal of Mathematics 2 Proceedings of the London Mathematical Society. Third Series 2 Transactions of the American Mathematical Society 2 Journal of the American Mathematical Society 2 IMRN. International Mathematics Research Notices 2 Experimental Mathematics 2 Annals of Mathematics. Second Series 2 Journal of the European Mathematical Society (JEMS) 2 The Quarterly Journal of Mathematics 2 Journal of the Australian Mathematical Society 2 Algebra & Number Theory 2 European Journal of Mathematics 2 Research in Number Theory 2 Proceedings of the American Mathematical Society. Series B 1 Bulletin of the Australian Mathematical Society 1 Discrete Mathematics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Periodica Mathematica Hungarica 1 The Mathematical Intelligencer 1 Bulletin. Classe des Sciences Mathématiques et Naturelles. Sciences Mathématiques 1 Canadian Journal of Mathematics 1 Duke Mathematical Journal 1 The Fibonacci Quarterly 1 Indagationes Mathematicae 1 Journal of Combinatorial Theory. Series A 1 Journal of the London Mathematical Society. Second Series 1 Mathematische Annalen 1 Mathematische Zeitschrift 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 SIAM Journal on Computing 1 Theoretical Computer Science 1 Utilitas Mathematica 1 Journal of Algorithms 1 Journal of Sichuan University. Natural Science Edition 1 Combinatorica 1 Acta Mathematica Hungarica 1 Journal of Cryptology 1 Aequationes Mathematicae 1 Glasnik Matematički. Serija III 1 Pokroky Matematiky, Fyziky & Astronomie 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Nieuw Archief voor Wiskunde. Vierde Serie 1 Indagationes Mathematicae. New Series 1 Philosophical Transactions of the Royal Society of London. Series A 1 Journal de Théorie des Nombres de Bordeaux 1 Congressus Numerantium 1 The New York Journal of Mathematics 1 Boletín de la Sociedad Matemática Mexicana. Third Series 1 RIMS Kokyuroku 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Pure and Applied Mathematics Quarterly 1 Lecture Notes in Computer Science 1 MAA Notes 1 Proceedings of Symposia in Applied Mathematics 1 Journal of Mathematical Cryptology 1 International Journal of Modern Mathematics 1 Uniform Distribution Theory 1 Albanian Journal of Mathematics 1 Involve 1 Moscow Journal of Combinatorics and Number Theory 1 Discrete Analysis 1 Transactions of the American Mathematical Society. Series B 1 De Gruyter Proceedings in Mathematics
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### Fields

 242 Number theory (11-XX) 16 Combinatorics (05-XX) 14 Computer science (68-XX) 13 Information and communication theory, circuits (94-XX) 11 General and overarching topics; collections (00-XX) 6 Algebraic geometry (14-XX) 5 Group theory and generalizations (20-XX) 3 History and biography (01-XX) 3 Partial differential equations (35-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Numerical analysis (65-XX) 2 Measure and integration (28-XX) 2 Convex and discrete geometry (52-XX) 1 Field theory and polynomials (12-XX) 1 Functions of a complex variable (30-XX) 1 Ordinary differential equations (34-XX) 1 Approximations and expansions (41-XX) 1 Geometry (51-XX) 1 Probability theory and stochastic processes (60-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

### Citations contained in zbMATH Open

199 Publications have been cited 1,796 times in 1,192 Documents Cited by Year
Prime numbers. A computational perspective. 2nd ed. Zbl 1088.11001
Crandall, Richard; Pomerance, Carl
2005
On a problem of Oppenheim concerning ”Factorisatio Numerorum”. Zbl 0513.10043
Canfield, E. R.; Erdős, Paul; Pomerance, Carl
1983
There are infinitely many Carmichael numbers. Zbl 0816.11005
Alford, W. R.; Granville, Andrew; Pomerance, Carl
1994
The Riemann zeta-function and the one-dimensional Weyl-Berry conjecture for fractal drums. Zbl 0739.34065
Lapidus, Michel L.; Pomerance, Carl
1993
On distinguishing prime numbers from composite numbers. Zbl 0526.10004
Adleman, Leonard M.; Pomerance, Carl; Rumely, Robert S.
1983
The pseudoprimes to $$25\cdot 10^9$$. Zbl 0444.10007
Pomerance, Carl; Selfridge, J. L.; Wagstaff, Samuel S. jun.
1980
A search for Wieferich and Wilson primes. Zbl 0854.11002
Crandall, Richard; Dilcher, Karl; Pomerance, Carl
1997
Factoring integers with the number field sieve. Zbl 0806.11067
Buhler, J. P.; Lenstra, H. W. jun.; Pomerance, Carl
1993
Popular values of Euler’s function. Zbl 0437.10001
Pomerance, Carl
1980
Carmichael’s lambda function. Zbl 0734.11047
Erdős, Paul; Pomerance, Carl; Schmutz, Eric
1991
On the normal number of prime factors of $$\phi(n)$$. Zbl 0617.10037
Erdős, Paul; Pomerance, Carl
1985
Counterexamples to the modified Weyl-Berry conjecture on fractal drums. Zbl 0858.58052
Lapidus, Michel L.; Pomerance, Carl
1996
On the distribution of amicable numbers. Zbl 0349.10004
Pomerance, Carl
1977
A rigorous time bound for factoring integers. Zbl 0770.11057
Lenstra, H. W. jun.; Pomerance, Carl
1992
Unusually large gaps between consecutive primes. Zbl 0706.11052
Maier, Helmut; Pomerance, Carl
1990
On the distribution of pseudoprimes. Zbl 0511.10002
Pomerance, Carl
1981
A note on the least prime in an arithmetic progression. Zbl 0436.10020
Pomerance, Carl
1980
Period of the power generator and small values of Carmichael’s function. Zbl 1029.11043
Friedlander, John B.; Pomerance, Carl; Shparlinski, Igor E.
2002
On primes recognizable in deterministic polynomial time. Zbl 0869.11102
Konyagin, Sergei; Pomerance, Carl
1997
On the binary expansions of algebraic numbers. Zbl 1076.11045
Bailey, David H.; Borwein, Jonathan M.; Crandall, Richard E.; Pomerance, Carl
2004
View-obstruction problems. III. Zbl 0563.10026
Cusick, T. W.; Pomerance, Carl
1984
Average case error estimates for the strong probable prime test. Zbl 0788.11059
Damgård, Ivan; Landrock, Peter; Pomerance, Carl
1993
Sieving by large integers and covering systems of congruences. Zbl 1210.11020
Filaseta, Michael; Ford, Kevin; Konyagin, Sergei; Pomerance, Carl; Yu, Gang
2007
Error estimates for the Davenport-Heilbronn theorems. Zbl 1227.11114
Belabas, Karim; Bhargava, Manjul; Pomerance, Carl
2010
Remarks on the Pólya-Vinogradov inequality. Zbl 1278.11080
Pomerance, Carl
2011
Analysis and comparison of some integer factoring algorithms. Zbl 0508.10004
Pomerance, C.
1982
Fonction zêta de Riemann et conjecture de Weyl-Berry pour les tambours fractals. (The Riemann zeta-function and the Weyl-Berry conjecture for fractal drums). Zbl 0707.58046
Lapidus, Michel L.; Pomerance, Carl
1990
On some problems of Mąkowski-Schinzel and Erdős concerning the arithmetical functions $$\varphi$$ and $$\sigma$$. Zbl 1027.11007
Luca, Florian; Pomerance, Carl
2002
On the periods of the linear congruential and power generators. Zbl 1080.11059
Kurlberg, Pär; Pomerance, Carl
2005
The role of smooth numbers in number theoretic algorithms. Zbl 0854.11047
Pomerance, Carl
1995
On numbers $$n$$ dividing the $$n$$th term of a linear recurrence. Zbl 1262.11015
Alba González, Juan José; Luca, Florian; Pomerance, Carl; Shparlinski, Igor E.
2012
On the largest prime factors of $$n$$ and $$n+1$$. Zbl 0379.10027
Erdős, Paul; Pomerance, Carl
1978
Multiply perfect numbers, Mersenne primes, and effective computability. Zbl 0324.10001
Pomerance, Carl
1977
A tale of two sieves. Zbl 1042.11529
Pomerance, Carl
1996
The expected number of random elements to generate a finite Abelian group. Zbl 0980.20079
Pomerance, Carl
2001
On locally repeated values of certain arithmetic functions. II. Zbl 0609.10034
Erdős, Paul; Pomerance, C.; Sárközy, A.
1987
On the difficulty of finding reliable witnesses. Zbl 0828.11074
Alford, W. R.; Granville, Andrew; Pomerance, Carl
1994
Combinatorial number theory. Zbl 0849.11001
Pomerance, Carl; Sárközy, András
1995
Fast, rigorous factorization and discrete logarithm algorithm. Zbl 0659.10003
Pomerance, Carl
1987
Two contradictory conjectures concerning Carmichael numbers. Zbl 0991.11067
Granville, Andrew; Pomerance, Carl
2002
On the largest prime factor of a Mersenne number. Zbl 1077.11003
Murata, Leo; Pomerance, Carl
2004
Heuristics for class numbers of prime-power real cyclotomic fields. Zbl 1106.11039
Buhler, Joe; Pomerance, Carl; Robertson, Leanne
2004
Prime numbers. A computational perspective. Zbl 0995.11072
Crandall, Richard; Pomerance, Carl
1999
Recent developments in primality testing. Zbl 0476.10004
Pomerance, Carl
1981
The quadratic sieve factoring algorithm. Zbl 0596.10006
Pomerance, Carl
1985
Odd perfect numbers are divisible by at least seven distinct primes. Zbl 0247.10007
Pomerance, Carl
1974
Smooth orders and cryptographic applications. Zbl 1058.11059
Pomerance, Carl; Shparlinski, Igor E.
2002
Divisors of the middle binomial coefficient. Zbl 1332.05005
Pomerance, Carl
2015
On the number of distinct values of Euler’s $$\varphi$$-function. Zbl 0638.10045
Maier, Helmut; Pomerance, Carl
1988
Implementation of the continued fraction integer factoring algorithm. Zbl 0556.10003
Pomerance, Carl; Wagstaff, Samuel S. jun.
1983
A hyperelliptic smoothness test. I. Zbl 0808.11073
Lenstra, H. W. jun.; Pila, J.; Pomerance, Carl
1993
Irreducible radical extensions and Euler-function chains. Zbl 1172.11029
Luca, Florian; Pomerance, Carl
2007
On Carmichael numbers in arithmetic progressions. Zbl 1208.11109
Banks, William D.; Pomerance, Carl
2010
On divisors of sums of integers. III. Zbl 0668.10055
Pomerance, Carl; Sárközy, A.; Stewart, C. L.
1988
On the problem of uniqueness for the maximum Stirling number(s) of the second kind. Zbl 1008.11006
Canfield, E. Rodney; Pomerance, Carl
2002
On the distribution in residue classes of integers with a fixed sum of digits. Zbl 1155.11345
Mauduit, Christian; Pomerance, Carl; Sárközy, András
2005
The distribution of Lucas and elliptic pseudoprimes. Zbl 0744.11066
Gordon, Daniel M.; Pomerance, Carl
1991
The distribution of smooth numbers in arithmetic progressions. Zbl 0752.11036
Balog, Antal; Pomerance, Carl
1992
Primality testing with Gaussian periods. Zbl 1429.11221
Lenstra, Hendrik W. jun.; Pomerance, Carl B.
2019
On the number of false witnesses for a composite number. Zbl 0586.10003
Erdős, Paul; Pomerance, Carl
1986
Fixed points for discrete logarithms. Zbl 1260.11004
Levin, Mariana; Pomerance, Carl; Soundararajan, K.
2010
Common values of the arithmetic functions $$\varphi$$ and $$\sigma$$. Zbl 1205.11010
Ford, Kevin; Luca, Florian; Pomerance, Carl
2010
On the normal behavior of the iterates of some arithmetic functions. Zbl 0721.11034
Erdős, Paul; Granville, A.; Pomerance, C.; Spiro, C.
1990
On the distribution of amicable numbers. II. Zbl 0448.10007
Pomerance, Carl
1981
On a problem of Arnold: the average multiplicative order of a given integer. Zbl 1282.11131
Kurlberg, Pär; Pomerance, Carl
2013
Reduction of huge, sparse matrices over finite fields via created catastrophes. Zbl 0771.65023
Pomerance, Carl; Smith, J. W.
1992
On sums involving reciprocals of the largest prime factor of an integer. Zbl 0615.10055
Erdős, Paul; Ivić, A.; Pomerance, C.
1986
The smallest n-uniform hypergraph with positive discrepancy. Zbl 0629.05053
Alon, N.; Kleitman, D. J.; Pomerance, C.; Saks, M.; Seymour, P.
1987
On the distribution of round numbers. Zbl 0565.10038
Pomerance, Carl
1985
On the smallest pseudopower. Zbl 1242.11006
Bourgain, Jean; Konyagin, Sergei V.; Pomerance, Carl; Shparlinski, Igor E.
2009
The generation of random numbers that are probably prime. Zbl 0669.10014
Beauchemin, Pierre; Brassard, Gilles; Crépeau, Claude; Goutier, Claude; Pomerance, Carl
1988
A hyperelliptic smoothness test. II. Zbl 0983.11072
Lenstra, H. W. jun.; Pila, J.; Pomerance, Carl
2002
Products of ratios of consecutive integers. Zbl 1155.11343
de la Bretèche, Régis; Pomerance, Carl; Tenenbaum, Gérald
2005
On the solutions to $$\varphi(n)=\varphi(n+k)$$. Zbl 0937.11037
Graham, S. W.; Holt, Jeffrey J.; Pomerance, Carl
1999
Proof of D. J. Newman’s coprime mapping conjecture. Zbl 0442.10003
Pomerance, Carl; Selfridge, J. L.
1980
Sets on which an entire function is determined by its range. Zbl 0473.30022
Diamond, Harold G.; Pomerance, Carl; Rubel, Lee
1981
Infinitude of elliptic Carmichael numbers. Zbl 1251.11004
Ekstrom, Aaron; Pomerance, Carl; Thakur, Dinesh S.
2012
On composite integers $$n$$ for which $$\varphi(n)\mid n-1$$. Zbl 1294.11005
Luca, Florian; Pomerance, Carl
2011
Some problems of Erdős on the sum-of-divisors function. Zbl 1365.11111
Pollack, Paul; Pomerance, Carl
2016
Lecture notes on primality testing and factoring. A short course at Kent State University, Canterbury, UK, June 16-18, 1983. Notes by Stephen M. Gagola, Jr. Zbl 0719.11002
Pomerance, Carl
1984
On locally repeated values of certain arithmetic functions. III. Zbl 0631.10029
Erdős, Paul; Pomerance, Carl; Sárközy, András
1987
A pipeline architecture for factoring large integers with the quadratic sieve algorithm. Zbl 0644.10002
Pomerance, Carl; Smith, J. W.; Tuler, Randy
1988
Some new results on odd perfect numbers. Zbl 0295.10005
Dandapat, G. G.; Hunsucker, J. L.; Pomerance, Carl
1975
The second largest prime factor of an odd perfect number. Zbl 0307.10009
Pomerance, Carl
1975
On the least prime in certain arithmetic progression. Zbl 0658.10049
Granville, Andrew; Pomerance, Carl
1990
Two methods in elementary analytic number theory. Zbl 0683.10003
Pomerance, Carl
1989
Euler’s function in residue classes. Zbl 0919.11006
Dence, Thomas; Pomerance, Carl
1998
Rigorous discrete logarithm computations in finite fields via smooth polynomials. Zbl 0915.11063
Bender, Renet Lovorn; Pomerance, Carl
1998
On the counting function of irregular primes. Zbl 1356.11067
Luca, Florian; Pizarro-Madariaga, Amalia; Pomerance, Carl
2015
On integers $$n$$ for which $$X^n-1$$ has a divisor of every degree. Zbl 1364.11143
Pomerance, Carl; Thompson, Lola; Weingartner, Andreas
2016
On the average number of divisors of the Euler function. Zbl 1127.11065
Luca, Florian; Pomerance, Carl
2007
Very short primality proofs. Zbl 0608.10002
Pomerance, Carl
1987
Estimates for certain sums involving the largest prime factor of an integer. Zbl 0546.10037
Ivić, A.; Pomerance, C.
1984
The Erdős conjecture for primitive sets. Zbl 1481.11026
Lichtman, Jared Duker; Pomerance, Carl
2019
On generalizing Artin’s conjecture on primitive roots to composite moduli. Zbl 1022.11049
Li, Shuguang; Pomerance, Carl
2003
Sets with prescribed arithmetic densities. Zbl 1212.11018
Luca, Florian; Pomerance, Carl; Porubský, Štefan
2008
Timed fair exchange of standard signatures (extended abstract). Zbl 1274.94068
Garay, Juan A.; Pomerance, Carl
2003
On the radical of a perfect number. Zbl 1230.11008
Luca, Florian; Pomerance, Carl
2010
Primality testing: variations on a theme of Lucas. Zbl 1203.11083
Pomerance, Carl
2010
On the number of divisors of $$n!$$. Zbl 0858.11051
Erdős, Paul; Graham, S. W.; Ivić, Aleksandar; Pomerance, Carl
1996
On primes and practical numbers. Zbl 07490456
Pomerance, Carl; Weingartner, Andreas
2022
Elliptic curves with Galois-stable cyclic subgroups of order 4. Zbl 1478.11084
Pomerance, Carl; Schaefer, Edward F.
2021
A note on Carmichael numbers in residue classes. Zbl 07497816
Pomerance, Carl
2021
Counting elliptic curves with an isogeny of degree three. Zbl 1483.11118
Pizzo, Maggie; Pomerance, Carl; Voight, John
2020
Phi, primorials, and Poisson. Zbl 1453.11123
Pollack, Paul; Pomerance, Carl
2020
Progress towards a nonintegrality conjecture. Zbl 1465.05007
Laishram, Shanta; López-Aguayo, Daniel; Pomerance, Carl; Thongjunthug, Thotsaphon
2020
Primality testing with Gaussian periods. Zbl 1429.11221
Lenstra, Hendrik W. jun.; Pomerance, Carl B.
2019
The Erdős conjecture for primitive sets. Zbl 1481.11026
Lichtman, Jared Duker; Pomerance, Carl
2019
The reciprocal sum of the amicable numbers. Zbl 1429.11009
Nguyen, Hanh My; Pomerance, Carl
2019
Primes in prime number races. Zbl 1473.11177
Lichtman, Jared Duker; Martin, Greg; Pomerance, Carl
2019
Proof of the Sheldon conjecture. Zbl 1473.11018
Pomerance, Carl; Spicer, Chris
2019
Symmetric primes revisited. Zbl 1462.11070
Banks, William; Pollack, Paul; Pomerance, Carl
2019
Counting integers with a smooth totient. Zbl 1475.11177
Banks, W. D.; Friedlander, J. B.; Pomerance, C.; Shparlinski, I. E.
2019
Divisor-sum fibers. Zbl 1410.11115
Pollack, Paul; Pomerance, Carl; Thompson, Lola
2018
Explicit estimates for the distribution of numbers free of large prime factors. Zbl 1433.11109
Lichtman, Jared D.; Pomerance, Carl
2018
The first function and its iterates. Zbl 1431.11010
Pomerance, Carl
2018
Density of singular pairs of integers. Zbl 1430.11134
Nedela, Roman; Pomerance, Carl
2018
The aliquot constant, after Bosma and Kane. Zbl 1445.11102
Pomerance, Carl
2018
Connected components of the graph generated by power maps in prime finite fields. Zbl 1441.05108
Pomerance, Carl; Shparlinksi, Igor E.
2018
Improved error bounds for the Fermat primality test on random inputs. Zbl 1441.11302
Lichtman, Jared Duker; Pomerance, Carl
2018
Squarefree smooth numbers and Euclidean prime generators. Zbl 1437.11007
Booker, Andrew R.; Pomerance, Carl
2017
Numbers divisible by a large shifted prime and large torsion subgroups of CM elliptic curves. Zbl 1405.11123
McNew, Nathan; Pollack, Paul; Pomerance, Carl
2017
Local behavior of the composition of the aliquot and co-totient functions. Zbl 1421.11076
Luca, Florian; Pomerance, Carl
2017
Triangles with prime hypotenuse. Zbl 1426.11095
Chow, Sam; Pomerance, Carl
2017
Some problems of Erdős on the sum-of-divisors function. Zbl 1365.11111
Pollack, Paul; Pomerance, Carl
2016
On integers $$n$$ for which $$X^n-1$$ has a divisor of every degree. Zbl 1364.11143
Pomerance, Carl; Thompson, Lola; Weingartner, Andreas
2016
Generating random factored Gaussian integers, easily. Zbl 1327.65009
Lebowitz-Lockard, Noah; Pomerance, Carl
2016
Divisors of the middle binomial coefficient. Zbl 1332.05005
Pomerance, Carl
2015
On the counting function of irregular primes. Zbl 1356.11067
Luca, Florian; Pizarro-Madariaga, Amalia; Pomerance, Carl
2015
The range of the sum-of-proper-divisors function. Zbl 1394.11007
Luca, Florian; Pomerance, Carl
2015
Sierpiński and Carmichael numbers. Zbl 1325.11010
Banks, William; Finch, Carrie; Luca, Florian; Pomerance, Carl; Stănică, Pantelimon
2015
Analytic number theory. In honor of Helmut Maier’s 60th birthday. Zbl 1336.11002
2015
On amicable numbers. Zbl 1395.11017
Pomerance, Carl
2015
A note on square totients. Zbl 1331.11085
Freiberg, Tristan; Pomerance, Carl
2015
The image of Carmichael’s $$\lambda$$-function. Zbl 1322.11104
Ford, Kevin; Luca, Florian; Pomerance, Carl
2014
Variant of a theorem of Erdős on the sum-of-proper-divisors function. Zbl 1297.11006
Pomerance, Carl; Yang, Hee-Sung
2014
Square values of Euler’s function. Zbl 1297.11125
Pollack, Paul; Pomerance, Carl
2014
On the local behavior of the order of appearance in the Fibonacci sequence. Zbl 1387.11016
Luca, Florian; Pomerance, Carl
2014
On the range of Carmichael’s universal-exponent function. Zbl 1292.11109
Luca, Florian; Pomerance, Carl
2014
On a problem of Arnold: the average multiplicative order of a given integer. Zbl 1282.11131
Kurlberg, Pär; Pomerance, Carl
2013
On congruences of the form $$\sigma(n)\equiv a\pmod n$$. Zbl 1271.11004
Anavi, Aria; Pollack, Paul; Pomerance, Carl
2013
On balanced subgroups of the multiplicative group. Zbl 1332.11089
Pomerance, Carl; Ulmer, Douglas
2013
On the distribution of some integers related to perfect and amicable numbers. Zbl 1285.11009
Pollack, Paul; Pomerance, Carl
2013
Sets of monotonicity for Euler’s totient function. Zbl 1348.11003
Pollack, Paul; Pomerance, Carl; Treviño, Enrique
2013
On numbers $$n$$ dividing the $$n$$th term of a linear recurrence. Zbl 1262.11015
Alba González, Juan José; Luca, Florian; Pomerance, Carl; Shparlinski, Igor E.
2012
Infinitude of elliptic Carmichael numbers. Zbl 1251.11004
Ekstrom, Aaron; Pomerance, Carl; Thakur, Dinesh S.
2012
Prime-perfect numbers. Zbl 1271.11006
Pollack, Paul; Pomerance, Carl
2012
Product-free sets with high density. Zbl 1357.11028
Kurlberg, Pär; Lagarias, Jeffrey C.; Pomerance, Carl
2012
The average order of elements in the multiplicative group of a finite field. Zbl 1285.11022
Hu, Yilan; Pomerance, Carl
2012
Remarks on the Pólya-Vinogradov inequality. Zbl 1278.11080
Pomerance, Carl
2011
On composite integers $$n$$ for which $$\varphi(n)\mid n-1$$. Zbl 1294.11005
Luca, Florian; Pomerance, Carl
2011
Primitive sets with large counting functions. Zbl 1249.11016
Martin, Greg; Pomerance, Carl
2011
Fibonacci integers. Zbl 1225.11022
Luca, Florian; Pomerance, Carl; Wagner, Stephan
2011
Error estimates for the Davenport-Heilbronn theorems. Zbl 1227.11114
Belabas, Karim; Bhargava, Manjul; Pomerance, Carl
2010
On Carmichael numbers in arithmetic progressions. Zbl 1208.11109
Banks, William D.; Pomerance, Carl
2010
Fixed points for discrete logarithms. Zbl 1260.11004
Levin, Mariana; Pomerance, Carl; Soundararajan, K.
2010
Common values of the arithmetic functions $$\varphi$$ and $$\sigma$$. Zbl 1205.11010
Ford, Kevin; Luca, Florian; Pomerance, Carl
2010
On the radical of a perfect number. Zbl 1230.11008
Luca, Florian; Pomerance, Carl
2010
Primality testing: variations on a theme of Lucas. Zbl 1203.11083
Pomerance, Carl
2010
On the distribution of pseudopowers. Zbl 1197.11004
Konyagin, Sergei V.; Pomerance, Carl; Shparlinski, Igor E.
2010
On the asymptotic effectiveness of Weil descent attacks. Zbl 1252.94080
Karabina, Koray; Menezes, Alfred; Pomerance, Carl; Shparlinski, Igor E.
2010
Rank statistics for a family of elliptic curves over a function field. Zbl 1200.14060
Pomerance, Carl; Shparlinski, Igor E.
2010
On the smallest pseudopower. Zbl 1242.11006
Bourgain, Jean; Konyagin, Sergei V.; Pomerance, Carl; Shparlinski, Igor E.
2009
On the distribution of sociable numbers. Zbl 1241.11120
Kobayashi, Mitsuo; Pollack, Paul; Pomerance, Carl
2009
A remark on Giuga’s conjecture and Lehmer’s totient problem. Zbl 1219.11003
Banks, William D.; Nevans, C. Wesley; Pomerance, Carl
2009
On the range of the iterated Euler function. Zbl 1184.11043
Luca, Florian; Pomerance, Carl
2009
On Giuga numbers. Zbl 1231.11115
Luca, Florian; Pomerance, Carl; Shparlinski, Igor
2009
On pseudosquares and pseudopowers. Zbl 1184.11026
Pomerance, Carl; Shparlinski, Igor E.
2009
Sets with prescribed arithmetic densities. Zbl 1212.11018
Luca, Florian; Pomerance, Carl; Porubský, Štefan
2008
On the proportion of numbers coprime to a given integer. Zbl 1175.11055
Erdős, Paul; Luca, Florian; Pomerance, Carl
2008
Smooth numbers and the quadratic sieve. Zbl 1188.11065
Pomerance, Carl
2008
Elementary thoughts on discrete logarithms. Zbl 1188.11070
Pomerance, Carl
2008
Sieving by large integers and covering systems of congruences. Zbl 1210.11020
Filaseta, Michael; Ford, Kevin; Konyagin, Sergei; Pomerance, Carl; Yu, Gang
2007
Irreducible radical extensions and Euler-function chains. Zbl 1172.11029
Luca, Florian; Pomerance, Carl
2007
On the average number of divisors of the Euler function. Zbl 1127.11065
Luca, Florian; Pomerance, Carl
2007
Maximal height of divisors of $$x^n-1$$. Zbl 1211.11108
Pomerance, Carl; Ryan, Nathan C.
2007
Prime numbers. A computational perspective. 2nd ed. Zbl 1088.11001
Crandall, Richard; Pomerance, Carl
2005
On the periods of the linear congruential and power generators. Zbl 1080.11059
Kurlberg, Pär; Pomerance, Carl
2005
On the distribution in residue classes of integers with a fixed sum of digits. Zbl 1155.11345
Mauduit, Christian; Pomerance, Carl; Sárközy, András
2005
Products of ratios of consecutive integers. Zbl 1155.11343
de la Bretèche, Régis; Pomerance, Carl; Tenenbaum, Gérald
2005
The iterated Carmichael $$\lambda$$-function and the number of cycles of the power generator. Zbl 1109.11046
Martin, Greg; Pomerance, Carl
2005
On the binary expansions of algebraic numbers. Zbl 1076.11045
Bailey, David H.; Borwein, Jonathan M.; Crandall, Richard E.; Pomerance, Carl
2004
On the largest prime factor of a Mersenne number. Zbl 1077.11003
Murata, Leo; Pomerance, Carl
2004
Heuristics for class numbers of prime-power real cyclotomic fields. Zbl 1106.11039
Buhler, Joe; Pomerance, Carl; Robertson, Leanne
2004
Multiplicative structure of values of the Euler function. Zbl 1099.11055
Banks, William D.; Friedlander, John B.; Pomerance, Carl; Shparlinski, Igor E.
2004
On generalizing Artin’s conjecture on primitive roots to composite moduli. Zbl 1022.11049
Li, Shuguang; Pomerance, Carl
2003
Timed fair exchange of standard signatures (extended abstract). Zbl 1274.94068
Garay, Juan A.; Pomerance, Carl
2003
Period of the power generator and small values of Carmichael’s function. Zbl 1029.11043
Friedlander, John B.; Pomerance, Carl; Shparlinski, Igor E.
2002
On some problems of Mąkowski-Schinzel and Erdős concerning the arithmetical functions $$\varphi$$ and $$\sigma$$. Zbl 1027.11007
Luca, Florian; Pomerance, Carl
2002
Two contradictory conjectures concerning Carmichael numbers. Zbl 0991.11067
Granville, Andrew; Pomerance, Carl
2002
Smooth orders and cryptographic applications. Zbl 1058.11059
Pomerance, Carl; Shparlinski, Igor E.
2002
On the problem of uniqueness for the maximum Stirling number(s) of the second kind. Zbl 1008.11006
Canfield, E. Rodney; Pomerance, Carl
2002
A hyperelliptic smoothness test. II. Zbl 0983.11072
Lenstra, H. W. jun.; Pila, J.; Pomerance, Carl
2002
Ruth-Aaron numbers revisited. Zbl 1051.11052
Pomerance, C.
2002
Primitive roots: a survey. Zbl 1175.11057
Li, Shuguang; Pomerance, Carl
2002
Primitive roots: a survey. Zbl 1132.11358
Li, Shuguang; Pomerance, Carl
2002
The expected number of random elements to generate a finite Abelian group. Zbl 0980.20079
Pomerance, Carl
2001
Small values of the Carmichael function and cryptographic applications. Zbl 0996.11075
Friedlander, John B.; Pomerance, Carl; Shparlinski, Igor E.
2001
Prime numbers. A computational perspective. Zbl 0995.11072
Crandall, Richard; Pomerance, Carl
1999
On the solutions to $$\varphi(n)=\varphi(n+k)$$. Zbl 0937.11037
Graham, S. W.; Holt, Jeffrey J.; Pomerance, Carl
1999
...and 99 more Documents
all top 5

### Cited by 1,279 Authors

 60 Pomerance, Carl Bernard 55 Shparlinski, Igor E. 51 Luca, Florian 34 Pollack, Paul 23 Lapidus, Michel L. 18 Banks, William D. 14 Ford, Kevin B. 12 Sanna, Carlo 11 Zhang, Zhenxiang 10 Elsholtz, Christian 10 Tenenbaum, Gérald 10 Žubrinić, Darko 9 Hajdu, Lajos 9 Konyagin, Sergeĭ Vladimirovich 9 Sun, Zhi-Wei 8 Bach, Eric 8 Sutherland, Andrew V. 8 Wagstaff, Samuel Standfield jun. 7 Grau, José María 7 Harvey, David I. 7 Kim, Sungjin 7 Lenstra, Hendrik W. jun. 7 Lichtman, Jared Duker 7 Moree, Pieter 6 Bailey, David Harold 6 Chen, Yonggao 6 Grantham, Jon 6 Granville, Andrew James 6 Lebowitz-Lockard, Noah 6 McNew, Nathan 6 Oller-Marcén, Antonio M. 6 Thomé, Emmanuel 6 Williams, Hugh Cowie 5 Berrizbeitia, Pedro 5 Bertók, Csanád 5 Borwein, Jonathan Michael 5 Bourgain, Jean 5 Bugeaud, Yann 5 Crandall, Richard E. 5 Dilcher, Karl 5 Friedlander, John Benjamin 5 Hildebrand, Adolf J. 5 Kinlaw, Paul A. 5 Kombrink, Sabrina 5 Martin, Greg 5 Nicolas, Jean-Louis 5 Nielsen, Pace P. 5 Radunović, Goran 5 Silverberg, Alice 5 Stănică, Pantelimon 5 Trudgian, Tim 5 Vu, Van H. 5 Winter, Steffen 4 Balister, Paul N. 4 Bayless, Jonathan 4 Bernstein, Daniel Julius 4 Bollobás, Béla 4 Bordignon, Matteo 4 Bröker, Reinier 4 Chen, Zhixiong 4 De Koninck, Jean-Marie 4 Dubickas, Artūras 4 Erdős, Pál 4 Freiberg, Tristan 4 Gao, Weidong 4 Ishmukhametov, Shamil 4 Jørgensen, Palle E. T. 4 Kátai, Imre 4 Kleinjung, Thorsten 4 Lauter, Kristin Estella 4 Lenstra, Arjen K. 4 Lucchini, Andrea 4 Maynard, James 4 Morain, François 4 Morris, Robert D. 4 Ostafe, Alina 4 Pan, Hao 4 Pappalardi, Francesco 4 Pintz, Janos 4 Rivoal, Tanguy 4 Rotkiewicz, Andrzej 4 Saradha, N. 4 Serra, Oriol 4 Sha, Min 4 Sorenson, Jonathan P. 4 Stewart, Cameron L. 4 Tao, Terence 4 te Riele, Herman 4 Treviño, Enrique 4 Wang, Zhiwei 4 Weingartner, Andreas J. 4 Wright, Thomas 4 Yamada, Tomohiro 4 Yau, Stephen Shing-Toung 3 Adamczewski, Boris 3 Alon, Noga M. 3 Andrica, Dorin 3 Atanassov, Krassimir Todorov 3 Balasubramanian, Ramachandran 3 Bhargava, Manjul ...and 1,179 more Authors
all top 5

### Cited in 234 Serials

 157 Mathematics of Computation 125 Journal of Number Theory 43 International Journal of Number Theory 29 Integers 27 Bulletin of the Australian Mathematical Society 26 Proceedings of the American Mathematical Society 24 The Ramanujan Journal 20 Journal de Théorie des Nombres de Bordeaux 15 Mathematika 15 Monatshefte für Mathematik 15 Transactions of the American Mathematical Society 15 Experimental Mathematics 14 Theoretical Computer Science 13 Discrete Mathematics 12 Acta Arithmetica 12 Acta Mathematica Hungarica 12 Journal of the Australian Mathematical Society 10 Rocky Mountain Journal of Mathematics 10 Advances in Mathematics 10 Journal of Cryptology 10 Designs, Codes and Cryptography 10 Journal of Integer Sequences 9 The Mathematical Intelligencer 9 Archiv der Mathematik 9 Indagationes Mathematicae. New Series 8 Mathematical Proceedings of the Cambridge Philosophical Society 8 Functiones et Approximatio. Commentarii Mathematici 8 Journal of Combinatorial Theory. Series A 8 Journal of Symbolic Computation 7 Journal of Mathematical Analysis and Applications 7 Michigan Mathematical Journal 7 Finite Fields and their Applications 7 Journal of Mathematical Cryptology 6 American Mathematical Monthly 6 Czechoslovak Mathematical Journal 6 Duke Mathematical Journal 6 Journal of Algebra 6 Journal of Complexity 6 Journal of the American Mathematical Society 6 Bulletin of the American Mathematical Society. New Series 6 Applicable Algebra in Engineering, Communication and Computing 5 Computers & Mathematics with Applications 5 Israel Journal of Mathematics 5 Mathematical Notes 5 Periodica Mathematica Hungarica 5 Chaos, Solitons and Fractals 5 Compositio Mathematica 5 Manuscripta Mathematica 5 Mathematische Annalen 5 Rendiconti del Circolo Matemàtico di Palermo. Serie II 5 European Journal of Combinatorics 5 Acta Applicandae Mathematicae 5 Annals of Mathematics. Second Series 5 Science China. Mathematics 4 International Journal of Mathematical Education in Science and Technology 4 Information Processing Letters 4 The Mathematical Gazette 4 Acta Mathematica 4 Bulletin of the London Mathematical Society 4 Canadian Mathematical Bulletin 4 Journal of Combinatorial Theory. Series B 4 Mathematica Slovaca 4 Mathematische Zeitschrift 4 Advances in Applied Mathematics 4 Ergodic Theory and Dynamical Systems 4 Linear Algebra and its Applications 4 Journal of Mathematical Sciences (New York) 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Communications in Mathematical Physics 3 Moscow University Mathematics Bulletin 3 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 3 Applied Mathematics and Computation 3 Inventiones Mathematicae 3 Proceedings of the Japan Academy. Series A 3 Algorithmica 3 Revista Matemática Iberoamericana 3 Applied Mathematics Letters 3 Elemente der Mathematik 3 International Journal of Computer Mathematics 3 Russian Mathematics 3 Electronic Research Announcements of the American Mathematical Society 3 Acta Mathematica Sinica. English Series 3 Lobachevskii Journal of Mathematics 3 JP Journal of Algebra, Number Theory and Applications 3 Advances in Mathematics of Communications 3 Acta Mathematica Universitatis Ostraviensis 3 Forum of Mathematics, Sigma 3 European Journal of Mathematics 2 Discrete Applied Mathematics 2 Reviews of Modern Physics 2 Annales de l’Institut Fourier 2 BIT 2 Colloquium Mathematicum 2 Geometriae Dedicata 2 Illinois Journal of Mathematics 2 Journal of Computational and Applied Mathematics 2 Journal of Computer and System Sciences 2 Journal of Functional Analysis 2 Mathematics and Computers in Simulation 2 Mathematische Nachrichten ...and 134 more Serials
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### Cited in 50 Fields

 1,010 Number theory (11-XX) 112 Information and communication theory, circuits (94-XX) 92 Computer science (68-XX) 87 Combinatorics (05-XX) 59 Measure and integration (28-XX) 48 Algebraic geometry (14-XX) 46 Group theory and generalizations (20-XX) 28 Probability theory and stochastic processes (60-XX) 25 Numerical analysis (65-XX) 24 Dynamical systems and ergodic theory (37-XX) 20 Quantum theory (81-XX) 15 Partial differential equations (35-XX) 14 Field theory and polynomials (12-XX) 12 Convex and discrete geometry (52-XX) 11 Commutative algebra (13-XX) 11 Global analysis, analysis on manifolds (58-XX) 10 Functions of a complex variable (30-XX) 10 Harmonic analysis on Euclidean spaces (42-XX) 9 Functional analysis (46-XX) 8 Operator theory (47-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 7 Ordinary differential equations (34-XX) 6 Real functions (26-XX) 5 History and biography (01-XX) 4 Differential geometry (53-XX) 4 General topology (54-XX) 4 Operations research, mathematical programming (90-XX) 4 Mathematics education (97-XX) 3 Mathematical logic and foundations (03-XX) 3 Associative rings and algebras (16-XX) 3 Sequences, series, summability (40-XX) 3 Approximations and expansions (41-XX) 3 Geometry (51-XX) 2 General and overarching topics; collections (00-XX) 2 Topological groups, Lie groups (22-XX) 2 Special functions (33-XX) 2 Abstract harmonic analysis (43-XX) 2 Manifolds and cell complexes (57-XX) 2 Statistics (62-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Category theory; homological algebra (18-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Algebraic topology (55-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Biology and other natural sciences (92-XX)

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