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Pomerance, Carl Bernard

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Author ID: pomerance.carl Recent zbMATH articles by "Pomerance, Carl Bernard"
Published as: Pomerance, C.; Pomerance, Carl; Pomerance, Carl B.; Pomerance, Carl Bernard
Homepage: https://www.math.dartmouth.edu/~carlp/
External Links: MGP · Math-Net.Ru · Wikidata · ORCID · ResearchGate · dblp · GND
Documents Indexed: 242 Publications since 1974, including 12 Books
Biographic References: 2 Publications
all top 5

Co-Authors

53 single-authored
24 Luca, Florian
21 Erdős, Pál
14 Pollack, Paul
13 Shparlinski, Igor E.
11 Sárközy, András
7 Nathanson, Melvyn Bernard
7 Nešetřil, Jaroslav
6 Ford, Kevin B.
6 Granville, Andrew James
6 Konyagin, Sergeĭ Vladimirovich
5 Banks, William D.
5 Kurlberg, Pär
5 Landman, Bruce M.
5 Lenstra, Hendrik W. jun.
5 Lichtman, Jared Duker
4 Crandall, Richard E.
4 Friedlander, John Benjamin
4 Ivić, Aleksandar P.
4 Li, Shuguang
4 Nowakowski, Richard J.
4 Penney, David E.
3 Alford, William Robert
3 Bateman, Paul Trevier
3 Canfield, E. Rodney
3 Hunsucker, John L.
3 Lagarias, Jeffrey C.
3 Lapidus, Michel L.
3 Maier, Helmut
3 Martin, Greg
3 Selfridge, John L.
2 Buhler, Joe P.
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 Smith, Joseph Wayne
2 Stewart, Cameron L.
2 Tenenbaum, Gérald
2 Thompson, Lola
2 Wagstaff, Samuel S. jun.
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 Chan, Tsz Ho
1 Cheng, Fred Yuanyou
1 Chow, Sam
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 Dilcher, Karl
1 Ekstrom, Aaron
1 Filaseta, Michael A.
1 Finch, Carrie E.
1 Fletcher, Peter
1 Franco, Zachary M.
1 Freiberg, Tristan
1 Garay, Juan A.
1 Goutier, Claude
1 Graham, Ronald Lewis
1 Holt, Jeffrey J.
1 Hu, Yilan
1 Karabina, Koray
1 Kim, Su Hee
1 Kinlaw, Paul A.
1 Kiss, Péter
1 Kleitman, Daniel J.
1 Kozek, Mark
1 Lacampagne, Carole B.
1 Laishram, Shanta
1 Landrock, Peter
1 Lebowitz-Lockard, Noah
1 Levin, Mariana E. Campbell
1 Lindgren, William F.
1 López-Aguayo, Daniel
1 Maynard, James
1 McNew, Nathan
1 Menezes, Alfred J.
1 Moreira, Carlos Gustavo Tamm de Araujo
1 Murata, Leo
...and 39 more Co-Authors
all top 5

Serials

21 Mathematics of Computation
17 Acta Arithmetica
13 Integers
11 Journal of Number Theory
6 Proceedings of the American Mathematical Society
6 The Ramanujan Journal
5 Mathematika
4 Colloquium Mathematicum
4 Publicationes Mathematicae
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
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 Notices of the American Mathematical Society
2 Annals of Mathematics. Second Series
2 Journal of the European Mathematical Society (JEMS)
2 Journal of the Australian Mathematical Society
2 Algebra & Number Theory
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 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 Experimental Mathematics
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 The Quarterly Journal of Mathematics
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 European Journal of Mathematics
1 Discrete Analysis
1 Transactions of the American Mathematical Society. Series B
1 De Gruyter Proceedings in Mathematics

Publications by Year

Citations contained in zbMATH Open

189 Publications have been cited 1,659 times in 1,093 Documents Cited by Year
Prime numbers. A computational perspective. 2nd ed. Zbl 1088.11001
Crandall, Richard; Pomerance, Carl
123
2005
On a problem of Oppenheim concerning ”Factorisatio Numerorum”. Zbl 0513.10043
Canfield, E. R.; Erdős, Paul; Pomerance, Carl
101
1983
There are infinitely many Carmichael numbers. Zbl 0816.11005
Alford, W. R.; Granville, Andrew; Pomerance, Carl
95
1994
The Riemann zeta-function and the one-dimensional Weyl-Berry conjecture for fractal drums. Zbl 0739.34065
Lapidus, Michel L.; Pomerance, Carl
56
1993
On distinguishing prime numbers from composite numbers. Zbl 0526.10004
Adleman, Leonard M.; Pomerance, Carl; Rumely, Robert S.
49
1983
A search for Wieferich and Wilson primes. Zbl 0854.11002
Crandall, Richard; Dilcher, Karl; Pomerance, Carl
45
1997
The pseudoprimes to \(25\cdot 10^9\). Zbl 0444.10007
Pomerance, Carl; Selfridge, J. L.; Wagstaff, Samuel S. jun.
43
1980
Factoring integers with the number field sieve. Zbl 0806.11067
Buhler, J. P.; Lenstra, H. W. jun.; Pomerance, Carl
35
1993
Popular values of Euler’s function. Zbl 0437.10001
Pomerance, Carl
27
1980
On the normal number of prime factors of \(\phi(n)\). Zbl 0617.10037
Erdős, Paul; Pomerance, Carl
26
1985
Carmichael’s lambda function. Zbl 0734.11047
Erdős, Paul; Pomerance, Carl; Schmutz, Eric
24
1991
Counterexamples to the modified Weyl-Berry conjecture on fractal drums. Zbl 0858.58052
Lapidus, Michel L.; Pomerance, Carl
23
1996
Period of the power generator and small values of Carmichael’s function. Zbl 1029.11043
Friedlander, John B.; Pomerance, Carl; Shparlinski, Igor E.
20
2002
A rigorous time bound for factoring integers. Zbl 0770.11057
Lenstra, H. W. jun.; Pomerance, Carl
20
1992
Unusually large gaps between consecutive primes. Zbl 0706.11052
Maier, Helmut; Pomerance, Carl
20
1990
On the distribution of amicable numbers. Zbl 0349.10004
Pomerance, Carl
20
1977
On primes recognizable in deterministic polynomial time. Zbl 0869.11102
Konyagin, Sergei; Pomerance, Carl
19
1997
A note on the least prime in an arithmetic progression. Zbl 0436.10020
Pomerance, Carl
19
1980
On the distribution of pseudoprimes. Zbl 0511.10002
Pomerance, Carl
18
1981
On the binary expansions of algebraic numbers. Zbl 1076.11045
Bailey, David H.; Borwein, Jonathan M.; Crandall, Richard E.; Pomerance, Carl
17
2004
Average case error estimates for the strong probable prime test. Zbl 0788.11059
Damgård, Ivan; Landrock, Peter; Pomerance, Carl
16
1993
Error estimates for the Davenport-Heilbronn theorems. Zbl 1227.11114
Belabas, Karim; Bhargava, Manjul; Pomerance, Carl
15
2010
On the periods of the linear congruential and power generators. Zbl 1080.11059
Kurlberg, Pär; Pomerance, Carl
15
2005
View-obstruction problems. III. Zbl 0563.10026
Cusick, T. W.; Pomerance, Carl
15
1984
On some problems of Mąkowski-Schinzel and Erdős concerning the arithmetical functions \(\varphi\) and \(\sigma\). Zbl 1027.11007
Luca, Florian; Pomerance, Carl
14
2002
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
14
1990
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.
13
2012
Fast, rigorous factorization and discrete logarithm algorithm. Zbl 0659.10003
Pomerance, Carl
13
1987
Analysis and comparison of some integer factoring algorithms. Zbl 0508.10004
Pomerance, C.
13
1982
The role of smooth numbers in number theoretic algorithms. Zbl 0854.11047
Pomerance, Carl
12
1995
On the normal behavior of the iterates of some arithmetic functions. Zbl 0721.11034
Erdős, Paul; Granville, A.; Pomerance, C.; Spiro, C.
12
1990
Multiply perfect numbers, Mersenne primes, and effective computability. Zbl 0324.10001
Pomerance, Carl
12
1977
Remarks on the Pólya-Vinogradov inequality. Zbl 1278.11080
Pomerance, Carl
11
2011
Sieving by large integers and covering systems of congruences. Zbl 1210.11020
Filaseta, Michael; Ford, Kevin; Konyagin, Sergei; Pomerance, Carl; Yu, Gang
11
2007
On the largest prime factor of a Mersenne number. Zbl 1077.11003
Murata, Leo; Pomerance, Carl
11
2004
Combinatorial number theory. Zbl 0849.11001
Pomerance, Carl; Sárközy, András
11
1995
Irreducible radical extensions and Euler-function chains. Zbl 1172.11029
Luca, Florian; Pomerance, Carl
10
2007
The expected number of random elements to generate a finite Abelian group. Zbl 0980.20079
Pomerance, Carl
10
2001
On the difficulty of finding reliable witnesses. Zbl 0828.11074
Alford, W. R.; Granville, Andrew; Pomerance, Carl
10
1994
On divisors of sums of integers. III. Zbl 0668.10055
Pomerance, Carl; Sárközy, A.; Stewart, C. L.
10
1988
On the largest prime factors of \(n\) and \(n+1\). Zbl 0379.10027
Erdős, Paul; Pomerance, Carl
10
1978
Odd perfect numbers are divisible by at least seven distinct primes. Zbl 0247.10007
Pomerance, Carl
10
1974
Divisors of the middle binomial coefficient. Zbl 1332.05005
Pomerance, Carl
9
2015
Heuristics for class numbers of prime-power real cyclotomic fields. Zbl 1106.11039
Buhler, Joe; Pomerance, Carl; Robertson, Leanne
9
2004
Smooth orders and cryptographic applications. Zbl 1058.11059
Pomerance, Carl; Shparlinski, Igor E.
9
2002
Two contradictory conjectures concerning Carmichael numbers. Zbl 0991.11067
Granville, Andrew; Pomerance, Carl
9
2002
A tale of two sieves. Zbl 1042.11529
Pomerance, Carl
9
1996
A hyperelliptic smoothness test. I. Zbl 0808.11073
Lenstra, H. W. jun.; Pila, J.; Pomerance, Carl
9
1993
On locally repeated values of certain arithmetic functions. II. Zbl 0609.10034
Erdős, Paul; Pomerance, C.; Sárközy, A.
9
1987
The quadratic sieve factoring algorithm. Zbl 0596.10006
Pomerance, Carl
9
1985
Recent developments in primality testing. Zbl 0476.10004
Pomerance, Carl
9
1981
On the distribution in residue classes of integers with a fixed sum of digits. Zbl 1155.11345
Mauduit, Christian; Pomerance, Carl; Sárközy, András
8
2005
On the problem of uniqueness for the maximum Stirling number(s) of the second kind. Zbl 1008.11006
Canfield, E. Rodney; Pomerance, Carl
8
2002
The distribution of smooth numbers in arithmetic progressions. Zbl 0752.11036
Balog, Antal; Pomerance, Carl
8
1992
On the number of distinct values of Euler’s \(\phi\)-function. Zbl 0638.10045
Maier, Helmut; Pomerance, Carl
8
1988
On the distribution of amicable numbers. II. Zbl 0448.10007
Pomerance, Carl
8
1981
On a problem of Arnold: the average multiplicative order of a given integer. Zbl 1282.11131
Kurlberg, Pär; Pomerance, Carl
7
2013
On composite integers \(n\) for which \(\varphi(n)\mid n-1\). Zbl 1294.11005
Luca, Florian; Pomerance, Carl
7
2011
Fixed points for discrete logarithms. Zbl 1260.11004
Levin, Mariana; Pomerance, Carl; Soundararajan, K.
7
2010
Common values of the arithmetic functions \(\varphi\) and \(\sigma\). Zbl 1205.11010
Ford, Kevin; Luca, Florian; Pomerance, Carl
7
2010
On the smallest pseudopower. Zbl 1242.11006
Bourgain, Jean; Konyagin, Sergei V.; Pomerance, Carl; Shparlinski, Igor E.
7
2009
Products of ratios of consecutive integers. Zbl 1155.11343
de la Bretèche, Régis; Pomerance, Carl; Tenenbaum, Gérald
7
2005
A hyperelliptic smoothness test. II. Zbl 0983.11072
Lenstra, H. W. jun.; Pila, J.; Pomerance, Carl
7
2002
On the solutions to \(\varphi(n)=\varphi(n+k)\). Zbl 0937.11037
Graham, S. W.; Holt, Jeffrey J.; Pomerance, Carl
7
1999
Reduction of huge, sparse matrices over finite fields via created catastrophes. Zbl 0771.65023
Pomerance, Carl; Smith, J. W.
7
1992
The distribution of Lucas and elliptic pseudoprimes. Zbl 0744.11066
Gordon, Daniel M.; Pomerance, Carl
7
1991
Two methods in elementary analytic number theory. Zbl 0683.10003
Pomerance, Carl
7
1989
The generation of random numbers that are probably prime. Zbl 0669.10014
Beauchemin, Pierre; Brassard, Gilles; Crépeau, Claude; Goutier, Claude; Pomerance, Carl
7
1988
On sums involving reciprocals of the largest prime factor of an integer. Zbl 0615.10055
Erdős, Paul; Ivić, A.; Pomerance, C.
7
1986
On the number of false witnesses for a composite number. Zbl 0586.10003
Erdős, Paul; Pomerance, Carl
7
1986
Implementation of the continued fraction integer factoring algorithm. Zbl 0556.10003
Pomerance, Carl; Wagstaff, Samuel S. jun.
7
1983
Sets on which an entire function is determined by its range. Zbl 0473.30022
Diamond, Harold G.; Pomerance, Carl; Rubel, Lee
7
1981
Primality testing with Gaussian periods. Zbl 1429.11221
Lenstra, Hendrik W. jun.; Pomerance, Carl B.
6
2019
Some problems of Erdős on the sum-of-divisors function. Zbl 1365.11111
Pollack, Paul; Pomerance, Carl
6
2016
Infinitude of elliptic Carmichael numbers. Zbl 1251.11004
Ekstrom, Aaron; Pomerance, Carl; Thakur, Dinesh S.
6
2012
Prime numbers. A computational perspective. Zbl 0995.11072
Crandall, Richard; Pomerance, Carl
6
1999
Rigorous discrete logarithm computations in finite fields via smooth polynomials. Zbl 0915.11063
Bender, Renet Lovorn; Pomerance, Carl
6
1998
Euler’s function in residue classes. Zbl 0919.11006
Dence, Thomas; Pomerance, Carl
6
1998
A pipeline architecture for factoring large integers with the quadratic sieve algorithm. Zbl 0644.10002
Pomerance, Carl; Smith, J. W.; Tuler, Randy
6
1988
The smallest n-uniform hypergraph with positive discrepancy. Zbl 0629.05053
Alon, N.; Kleitman, D. J.; Pomerance, C.; Saks, M.; Seymour, P.
6
1987
On the distribution of round numbers. Zbl 0565.10038
Pomerance, Carl
6
1985
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
6
1984
On composite \(n\) for which \(\varphi(n)\mid n-1\). II. Zbl 0328.10006
Pomerance, Carl
6
1977
The second largest prime factor of an odd perfect number. Zbl 0307.10009
Pomerance, Carl
6
1975
Explicit estimates for the distribution of numbers free of large prime factors. Zbl 1433.11109
Lichtman, Jared D.; Pomerance, Carl
5
2018
On integers \(n\) for which \(X^n-1\) has a divisor of every degree. Zbl 1364.11143
Pomerance, Carl; Thompson, Lola; Weingartner, Andreas
5
2016
On the counting function of irregular primes. Zbl 1356.11067
Luca, Florian; Pizarro-Madariaga, Amalia; Pomerance, Carl
5
2015
On congruences of the form \(\sigma(n)\equiv a\pmod n\). Zbl 1271.11004
Anavi, Aria; Pollack, Paul; Pomerance, Carl
5
2013
On Carmichael numbers in arithmetic progressions. Zbl 1208.11109
Banks, William D.; Pomerance, Carl
5
2010
On the distribution of sociable numbers. Zbl 1241.11120
Kobayashi, Mitsuo; Pollack, Paul; Pomerance, Carl
5
2009
On the average number of divisors of the Euler function. Zbl 1127.11065
Luca, Florian; Pomerance, Carl
5
2007
The iterated Carmichael \(\lambda\)-function and the number of cycles of the power generator. Zbl 1109.11046
Martin, Greg; Pomerance, Carl
5
2005
Timed fair exchange of standard signatures (extended abstract). Zbl 1274.94068
Garay, Juan A.; Pomerance, Carl
5
2003
On generalizing Artin’s conjecture on primitive roots to composite moduli. Zbl 1022.11049
Li, Shuguang; Pomerance, Carl
5
2003
On the number of divisors of \(n!\). Zbl 0858.11051
Erdős, Paul; Graham, S. W.; Ivić, Aleksandar; Pomerance, Carl
5
1996
On the least prime in certain arithmetic progression. Zbl 0658.10049
Granville, Andrew; Pomerance, Carl
5
1990
Very short primality proofs. Zbl 0608.10002
Pomerance, Carl
5
1987
On the longest simple path in the divisor graph. Zbl 0546.05038
Pomerance, Carl
5
1983
Proof of D. J. Newman’s coprime mapping conjecture. Zbl 0442.10003
Pomerance, Carl; Selfridge, J. L.
5
1980
The prime number graph. Zbl 0396.10002
Pomerance, Carl
5
1979
Counting elliptic curves with an isogeny of degree three. Zbl 07177262
Pizzo, Maggie; Pomerance, Carl; Voight, John
1
2020
Primality testing with Gaussian periods. Zbl 1429.11221
Lenstra, Hendrik W. jun.; Pomerance, Carl B.
6
2019
The reciprocal sum of the amicable numbers. Zbl 1429.11009
Nguyen, Hanh My; Pomerance, Carl
4
2019
The Erdős conjecture for primitive sets. Zbl 07046192
Lichtman, Jared Duker; Pomerance, Carl
3
2019
Symmetric primes revisited. Zbl 07133445
Banks, William; Pollack, Paul; Pomerance, Carl
1
2019
Proof of the Sheldon conjecture. Zbl 07109913
Pomerance, Carl; Spicer, Chris
1
2019
Primes in prime number races. Zbl 07102537
Lichtman, Jared Duker; Martin, Greg; Pomerance, Carl
1
2019
Explicit estimates for the distribution of numbers free of large prime factors. Zbl 1433.11109
Lichtman, Jared D.; Pomerance, Carl
5
2018
Divisor-sum fibers. Zbl 1410.11115
Pollack, Paul; Pomerance, Carl; Thompson, Lola
4
2018
Density of singular pairs of integers. Zbl 1430.11134
Nedela, Roman; Pomerance, Carl
1
2018
The first function and its iterates. Zbl 1431.11010
Pomerance, Carl
1
2018
The aliquot constant, after Bosma and Kane. Zbl 1445.11102
Pomerance, Carl
1
2018
Numbers divisible by a large shifted prime and large torsion subgroups of CM elliptic curves. Zbl 1405.11123
McNew, Nathan; Pollack, Paul; Pomerance, Carl
3
2017
Local behavior of the composition of the aliquot and co-totient functions. Zbl 1421.11076
Luca, Florian; Pomerance, Carl
1
2017
Squarefree smooth numbers and Euclidean prime generators. Zbl 1437.11007
Booker, Andrew R.; Pomerance, Carl
1
2017
Triangles with prime hypotenuse. Zbl 1426.11095
Chow, Sam; Pomerance, Carl
1
2017
Some problems of Erdős on the sum-of-divisors function. Zbl 1365.11111
Pollack, Paul; Pomerance, Carl
6
2016
On integers \(n\) for which \(X^n-1\) has a divisor of every degree. Zbl 1364.11143
Pomerance, Carl; Thompson, Lola; Weingartner, Andreas
5
2016
Generating random factored Gaussian integers, easily. Zbl 1327.65009
Lebowitz-Lockard, Noah; Pomerance, Carl
1
2016
Divisors of the middle binomial coefficient. Zbl 1332.05005
Pomerance, Carl
9
2015
On the counting function of irregular primes. Zbl 1356.11067
Luca, Florian; Pizarro-Madariaga, Amalia; Pomerance, Carl
5
2015
Sierpiński and Carmichael numbers. Zbl 1325.11010
Banks, William; Finch, Carrie; Luca, Florian; Pomerance, Carl; Stănică, Pantelimon
3
2015
On amicable numbers. Zbl 1395.11017
Pomerance, Carl
2
2015
Analytic number theory. In honor of Helmut Maier’s 60th birthday. Zbl 1336.11002
Pomerance, Carl (ed.); Rassias, Michael Th. (ed.)
2
2015
The range of the sum-of-proper-divisors function. Zbl 1394.11007
Luca, Florian; Pomerance, Carl
2
2015
A note on square totients. Zbl 1331.11085
Freiberg, Tristan; Pomerance, Carl
1
2015
The image of Carmichael’s \(\lambda\)-function. Zbl 1322.11104
Ford, Kevin; Luca, Florian; Pomerance, Carl
3
2014
Variant of a theorem of Erdős on the sum-of-proper-divisors function. Zbl 1297.11006
Pomerance, Carl; Yang, Hee-Sung
3
2014
Square values of Euler’s function. Zbl 1297.11125
Pollack, Paul; Pomerance, Carl
2
2014
On the local behavior of the order of appearance in the Fibonacci sequence. Zbl 1387.11016
Luca, Florian; Pomerance, Carl
1
2014
On the range of Carmichael’s universal-exponent function. Zbl 1292.11109
Luca, Florian; Pomerance, Carl
1
2014
On a problem of Arnold: the average multiplicative order of a given integer. Zbl 1282.11131
Kurlberg, Pär; Pomerance, Carl
7
2013
On congruences of the form \(\sigma(n)\equiv a\pmod n\). Zbl 1271.11004
Anavi, Aria; Pollack, Paul; Pomerance, Carl
5
2013
On balanced subgroups of the multiplicative group. Zbl 1332.11089
Pomerance, Carl; Ulmer, Douglas
4
2013
On the distribution of some integers related to perfect and amicable numbers. Zbl 1285.11009
Pollack, Paul; Pomerance, Carl
3
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.
13
2012
Infinitude of elliptic Carmichael numbers. Zbl 1251.11004
Ekstrom, Aaron; Pomerance, Carl; Thakur, Dinesh S.
6
2012
Prime-perfect numbers. Zbl 1271.11006
Pollack, Paul; Pomerance, Carl
3
2012
The average order of elements in the multiplicative group of a finite field. Zbl 1285.11022
Hu, Yilan; Pomerance, Carl
1
2012
Product-free sets with high density. Zbl 1357.11028
Kurlberg, Pär; Lagarias, Jeffrey C.; Pomerance, Carl
1
2012
Remarks on the Pólya-Vinogradov inequality. Zbl 1278.11080
Pomerance, Carl
11
2011
On composite integers \(n\) for which \(\varphi(n)\mid n-1\). Zbl 1294.11005
Luca, Florian; Pomerance, Carl
7
2011
Primitive sets with large counting functions. Zbl 1249.11016
Martin, Greg; Pomerance, Carl
2
2011
Fibonacci integers. Zbl 1225.11022
Luca, Florian; Pomerance, Carl; Wagner, Stephan
1
2011
Error estimates for the Davenport-Heilbronn theorems. Zbl 1227.11114
Belabas, Karim; Bhargava, Manjul; Pomerance, Carl
15
2010
Fixed points for discrete logarithms. Zbl 1260.11004
Levin, Mariana; Pomerance, Carl; Soundararajan, K.
7
2010
Common values of the arithmetic functions \(\varphi\) and \(\sigma\). Zbl 1205.11010
Ford, Kevin; Luca, Florian; Pomerance, Carl
7
2010
On Carmichael numbers in arithmetic progressions. Zbl 1208.11109
Banks, William D.; Pomerance, Carl
5
2010
Primality testing: variations on a theme of Lucas. Zbl 1203.11083
Pomerance, Carl
4
2010
On the radical of a perfect number. Zbl 1230.11008
Luca, Florian; Pomerance, Carl
3
2010
On the distribution of pseudopowers. Zbl 1197.11004
Konyagin, Sergei V.; Pomerance, Carl; Shparlinski, Igor E.
3
2010
On the asymptotic effectiveness of Weil descent attacks. Zbl 1252.94080
Karabina, Koray; Menezes, Alfred; Pomerance, Carl; Shparlinski, Igor E.
1
2010
Rank statistics for a family of elliptic curves over a function field. Zbl 1200.14060
Pomerance, Carl; Shparlinski, Igor E.
1
2010
On the smallest pseudopower. Zbl 1242.11006
Bourgain, Jean; Konyagin, Sergei V.; Pomerance, Carl; Shparlinski, Igor E.
7
2009
On the distribution of sociable numbers. Zbl 1241.11120
Kobayashi, Mitsuo; Pollack, Paul; Pomerance, Carl
5
2009
A remark on Giuga’s conjecture and Lehmer’s totient problem. Zbl 1219.11003
Banks, William D.; Nevans, C. Wesley; Pomerance, Carl
3
2009
On Giuga numbers. Zbl 1231.11115
Luca, Florian; Pomerance, Carl; Shparlinski, Igor
2
2009
On the range of the iterated Euler function. Zbl 1184.11043
Luca, Florian; Pomerance, Carl
2
2009
On pseudosquares and pseudopowers. Zbl 1184.11026
Pomerance, Carl; Shparlinski, Igor E.
1
2009
Sets with prescribed arithmetic densities. Zbl 1212.11018
Luca, Florian; Pomerance, Carl; Porubský, Štefan
4
2008
On the proportion of numbers coprime to a given integer. Zbl 1175.11055
Erdős, Paul; Luca, Florian; Pomerance, Carl
4
2008
Smooth numbers and the quadratic sieve. Zbl 1188.11065
Pomerance, Carl
3
2008
Elementary thoughts on discrete logarithms. Zbl 1188.11070
Pomerance, Carl
2
2008
Sieving by large integers and covering systems of congruences. Zbl 1210.11020
Filaseta, Michael; Ford, Kevin; Konyagin, Sergei; Pomerance, Carl; Yu, Gang
11
2007
Irreducible radical extensions and Euler-function chains. Zbl 1172.11029
Luca, Florian; Pomerance, Carl
10
2007
On the average number of divisors of the Euler function. Zbl 1127.11065
Luca, Florian; Pomerance, Carl
5
2007
Maximal height of divisors of \(x^n-1\). Zbl 1211.11108
Pomerance, Carl; Ryan, Nathan C.
4
2007
Prime numbers. A computational perspective. 2nd ed. Zbl 1088.11001
Crandall, Richard; Pomerance, Carl
123
2005
On the periods of the linear congruential and power generators. Zbl 1080.11059
Kurlberg, Pär; Pomerance, Carl
15
2005
On the distribution in residue classes of integers with a fixed sum of digits. Zbl 1155.11345
Mauduit, Christian; Pomerance, Carl; Sárközy, András
8
2005
Products of ratios of consecutive integers. Zbl 1155.11343
de la Bretèche, Régis; Pomerance, Carl; Tenenbaum, Gérald
7
2005
The iterated Carmichael \(\lambda\)-function and the number of cycles of the power generator. Zbl 1109.11046
Martin, Greg; Pomerance, Carl
5
2005
On the binary expansions of algebraic numbers. Zbl 1076.11045
Bailey, David H.; Borwein, Jonathan M.; Crandall, Richard E.; Pomerance, Carl
17
2004
On the largest prime factor of a Mersenne number. Zbl 1077.11003
Murata, Leo; Pomerance, Carl
11
2004
Heuristics for class numbers of prime-power real cyclotomic fields. Zbl 1106.11039
Buhler, Joe; Pomerance, Carl; Robertson, Leanne
9
2004
Multiplicative structure of values of the Euler function. Zbl 1099.11055
Banks, William D.; Friedlander, John B.; Pomerance, Carl; Shparlinski, Igor E.
4
2004
Timed fair exchange of standard signatures (extended abstract). Zbl 1274.94068
Garay, Juan A.; Pomerance, Carl
5
2003
On generalizing Artin’s conjecture on primitive roots to composite moduli. Zbl 1022.11049
Li, Shuguang; Pomerance, Carl
5
2003
Period of the power generator and small values of Carmichael’s function. Zbl 1029.11043
Friedlander, John B.; Pomerance, Carl; Shparlinski, Igor E.
20
2002
On some problems of Mąkowski-Schinzel and Erdős concerning the arithmetical functions \(\varphi\) and \(\sigma\). Zbl 1027.11007
Luca, Florian; Pomerance, Carl
14
2002
Smooth orders and cryptographic applications. Zbl 1058.11059
Pomerance, Carl; Shparlinski, Igor E.
9
2002
Two contradictory conjectures concerning Carmichael numbers. Zbl 0991.11067
Granville, Andrew; Pomerance, Carl
9
2002
On the problem of uniqueness for the maximum Stirling number(s) of the second kind. Zbl 1008.11006
Canfield, E. Rodney; Pomerance, Carl
8
2002
A hyperelliptic smoothness test. II. Zbl 0983.11072
Lenstra, H. W. jun.; Pila, J.; Pomerance, Carl
7
2002
Ruth-Aaron numbers revisited. Zbl 1051.11052
Pomerance, C.
2
2002
Primitive roots: a survey. Zbl 1132.11358
Li, Shuguang; Pomerance, Carl
1
2002
Primitive roots: a survey. Zbl 1175.11057
Li, Shuguang; Pomerance, Carl
1
2002
The expected number of random elements to generate a finite Abelian group. Zbl 0980.20079
Pomerance, Carl
10
2001
Small values of the Carmichael function and cryptographic applications. Zbl 0996.11075
Friedlander, John B.; Pomerance, Carl; Shparlinski, Igor E.
1
2001
On the solutions to \(\varphi(n)=\varphi(n+k)\). Zbl 0937.11037
Graham, S. W.; Holt, Jeffrey J.; Pomerance, Carl
7
1999
Prime numbers. A computational perspective. Zbl 0995.11072
Crandall, Richard; Pomerance, Carl
6
1999
Residue classes free of values of Euler’s function. Zbl 0931.11037
Ford, Kevin; Konyagin, Sergei; Pomerance, Carl
4
1999
Rigorous discrete logarithm computations in finite fields via smooth polynomials. Zbl 0915.11063
Bender, Renet Lovorn; Pomerance, Carl
6
1998
Euler’s function in residue classes. Zbl 0919.11006
Dence, Thomas; Pomerance, Carl
6
1998
A search for Wieferich and Wilson primes. Zbl 0854.11002
Crandall, Richard; Dilcher, Karl; Pomerance, Carl
45
1997
On primes recognizable in deterministic polynomial time. Zbl 0869.11102
Konyagin, Sergei; Pomerance, Carl
19
1997
Automaticity. II: Descriptional complexity in the unary case. Zbl 0959.11015
Pomerance, Carl; Robson, John Michael; Shallit, Jeffrey
4
1997
Counterexamples to the modified Weyl-Berry conjecture on fractal drums. Zbl 0858.58052
Lapidus, Michel L.; Pomerance, Carl
23
1996
A tale of two sieves. Zbl 1042.11529
Pomerance, Carl
9
1996
On the number of divisors of \(n!\). Zbl 0858.11051
Erdős, Paul; Graham, S. W.; Ivić, Aleksandar; Pomerance, Carl
5
1996
...and 89 more Documents
all top 5

Cited by 1,199 Authors

55 Shparlinski, Igor E.
53 Pomerance, Carl Bernard
50 Luca, Florian
31 Pollack, Paul
22 Lapidus, Michel L.
19 Banks, William D.
13 Ford, Kevin B.
11 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 Sutherland, Andrew V.
7 Bach, Eric
7 Grau, José María
7 Lenstra, Hendrik W. jun.
7 Moree, Pieter
6 Bailey, David Harold
6 Granville, Andrew James
6 Kim, Sungjin
6 McNew, Nathan
6 Oller-Marcén, Antonio M.
5 Berrizbeitia, Pedro
5 Bertók, Csanád
5 Borwein, Jonathan Michael
5 Bourgain, Jean
5 Bugeaud, Yann
5 Chen, Yonggao
5 Crandall, Richard E.
5 Dilcher, Karl
5 Friedlander, John Benjamin
5 Gao, Weidong
5 Grantham, Jon
5 Harvey, David I.
5 Hildebrand, Adolf J.
5 Nicolas, Jean-Louis
5 Nielsen, Pace P.
5 Radunović, Goran
5 Silverberg, Alice
5 Sorenson, Jonathan P.
5 Stănică, Pantelimon
5 Thomé, Emmanuel
5 Trudgian, Tim
5 Vu, Van H.
5 Williams, Hugh Cowie
5 Winter, Steffen
4 Bernstein, Daniel Julius
4 Bröker, Reinier
4 De Koninck, Jean-Marie
4 Deng, Lih-Yuan
4 Erdős, Pál
4 Freiberg, Tristan
4 Ishmukhametov, Shamil
4 Jørgensen, Palle E. T.
4 Kátai, Imre
4 Kinlaw, Paul A.
4 Kombrink, Sabrina
4 Lauter, Kristin Estella
4 Lenstra, Arjen K.
4 Lichtman, Jared Duker
4 Lucchini, Andrea
4 Martin, Greg
4 Maynard, James
4 Ostafe, Alina
4 Pappalardi, Francesco
4 Pintz, Janos
4 Rivoal, Tanguy
4 Rotkiewicz, Andrzej
4 Saradha, N.
4 Sha, Min
4 Stewart, Cameron L.
4 Tao, Terence
4 te Riele, Herman
4 Wagstaff, Samuel S. jun.
4 Wang, Zhiwei
4 Wright, Thomas
4 Yamada, Tomohiro
4 Yau, Stephen Shing-Toung
3 Adamczewski, Boris
3 Alon, Noga M.
3 Atanassov, Krassimir Todorov
3 Bayless, Jonathan
3 Bhargava, Manjul
3 Bisson, Gaetan
3 Broughan, Kevin A.
3 Chen, Zhixiong
3 Cho, Peter Jaehyun
3 Coppersmith, Don
3 Croot, Ernie
3 Czerwiński, Sebastian
3 Defant, Colin
3 Du, Xiaoni
3 Dubickas, Artūras
3 Dutkay, Dorin Ervin
3 Garcia, Stephan Ramon
3 Gaudry, Pierrick
3 Ghanmi, Nejib
...and 1,099 more Authors
all top 5

Cited in 215 Serials

152 Mathematics of Computation
122 Journal of Number Theory
40 International Journal of Number Theory
26 Bulletin of the Australian Mathematical Society
24 Proceedings of the American Mathematical Society
19 The Ramanujan Journal
19 Integers
18 Journal de Théorie des Nombres de Bordeaux
15 Mathematika
15 Monatshefte für Mathematik
15 Theoretical Computer Science
15 Transactions of the American Mathematical Society
14 Experimental Mathematics
13 Discrete Mathematics
12 Journal of the Australian Mathematical Society
11 Acta Arithmetica
10 Rocky Mountain Journal of Mathematics
10 Acta Mathematica Hungarica
10 Journal of Cryptology
10 Designs, Codes and Cryptography
9 The Mathematical Intelligencer
9 Advances in Mathematics
9 Indagationes Mathematicae. New Series
9 Journal of Integer Sequences
8 Archiv der Mathematik
8 Functiones et Approximatio. Commentarii Mathematici
8 Journal of Combinatorial Theory. Series A
7 Information Processing Letters
7 Mathematical Proceedings of the Cambridge Philosophical Society
7 Michigan Mathematical Journal
7 Journal of Symbolic Computation
7 Journal of Mathematical Cryptology
6 American Mathematical Monthly
6 Journal of Mathematical Analysis and Applications
6 Czechoslovak Mathematical Journal
6 Duke Mathematical Journal
6 Journal of Complexity
6 Journal of the American Mathematical Society
6 Bulletin of the American Mathematical Society. New Series
6 Finite Fields and their Applications
5 Computers & Mathematics with Applications
5 Israel Journal of Mathematics
5 Periodica Mathematica Hungarica
5 Chaos, Solitons and Fractals
5 Compositio Mathematica
5 Journal of Algebra
5 Manuscripta Mathematica
5 Mathematische Annalen
5 Rendiconti del Circolo Matemàtico di Palermo. Serie II
5 European Journal of Combinatorics
5 Applicable Algebra in Engineering, Communication and Computing
5 Annals of Mathematics. Second Series
5 Science China. Mathematics
4 The Mathematical Gazette
4 Mathematical Notes
4 Acta Mathematica
4 Bulletin of the London Mathematical Society
4 Journal of Combinatorial Theory. Series B
4 Journal of Computational and Applied Mathematics
4 Mathematica Slovaca
4 Advances in Applied Mathematics
4 Ergodic Theory and Dynamical Systems
4 Acta Applicandae Mathematicae
4 Linear Algebra and its Applications
3 Communications in Mathematical Physics
3 International Journal of Mathematical Education in Science and Technology
3 Moscow University Mathematics Bulletin
3 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
3 Applied Mathematics and Computation
3 Mathematische Zeitschrift
3 Proceedings of the Japan Academy. Series A
3 Algorithmica
3 Information and Computation
3 Applied Mathematics Letters
3 International Journal of Computer Mathematics
3 Russian Mathematics
3 Journal of Mathematical Sciences (New York)
3 Electronic Research Announcements of the American Mathematical Society
3 Acta Mathematica Sinica. English Series
3 Lobachevskii Journal of Mathematics
3 Comptes Rendus. Mathématique. Académie des Sciences, Paris
3 Advances in Mathematics of Communications
3 Acta Mathematica Universitatis Ostraviensis
3 Forum of Mathematics, Sigma
2 Discrete Applied Mathematics
2 Reviews of Modern Physics
2 Annales de l’Institut Fourier
2 BIT
2 Canadian Mathematical Bulletin
2 Geometriae Dedicata
2 Illinois Journal of Mathematics
2 Inventiones Mathematicae
2 Journal of Computer and System Sciences
2 Journal of Functional Analysis
2 Mathematische Nachrichten
2 Topology and its Applications
2 Statistics & Probability Letters
2 Revista Matemática Iberoamericana
2 Journal of Theoretical Probability
2 The Journal of Supercomputing
...and 115 more Serials
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Cited in 49 Fields

920 Number theory (11-XX)
101 Information and communication theory, circuits (94-XX)
90 Computer science (68-XX)
78 Combinatorics (05-XX)
56 Measure and integration (28-XX)
44 Algebraic geometry (14-XX)
43 Group theory and generalizations (20-XX)
27 Probability theory and stochastic processes (60-XX)
24 Numerical analysis (65-XX)
22 Dynamical systems and ergodic theory (37-XX)
18 Quantum theory (81-XX)
13 Field theory and polynomials (12-XX)
13 Partial differential equations (35-XX)
11 Convex and discrete geometry (52-XX)
11 Global analysis, analysis on manifolds (58-XX)
10 Commutative algebra (13-XX)
10 Functions of a complex variable (30-XX)
10 Harmonic analysis on Euclidean spaces (42-XX)
9 Functional analysis (46-XX)
7 Linear and multilinear algebra; matrix theory (15-XX)
7 Real functions (26-XX)
7 Operator theory (47-XX)
6 History and biography (01-XX)
6 Ordinary differential equations (34-XX)
4 General and overarching topics; collections (00-XX)
4 Sequences, series, summability (40-XX)
4 Differential geometry (53-XX)
4 General topology (54-XX)
4 Operations research, mathematical programming (90-XX)
3 Mathematical logic and foundations (03-XX)
3 Approximations and expansions (41-XX)
3 Geometry (51-XX)
3 Mathematics education (97-XX)
2 Associative rings and algebras (16-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)
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 Integral transforms, operational calculus (44-XX)
1 Algebraic topology (55-XX)
1 Fluid mechanics (76-XX)
1 Statistical mechanics, structure of matter (82-XX)
1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
1 Biology and other natural sciences (92-XX)

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