Edit Profile Pomerance, Carl Bernard Compute Distance To: Compute Author ID: pomerance.carl 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 all top 5 Fields 233 Number theory (11-XX) 16 Combinatorics (05-XX) 14 Computer science (68-XX) 12 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 Partial differential equations (35-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Numerical analysis (65-XX) 2 History and biography (01-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) Publications by Year all cited Publications top 5 cited Publications 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 1088.11001Crandall, Richard; Pomerance, Carl 123 2005 On a problem of Oppenheim concerning ”Factorisatio Numerorum”. Zbl 0513.10043Canfield, E. R.; Erdős, Paul; Pomerance, Carl 101 1983 There are infinitely many Carmichael numbers. Zbl 0816.11005Alford, W. R.; Granville, Andrew; Pomerance, Carl 95 1994 The Riemann zeta-function and the one-dimensional Weyl-Berry conjecture for fractal drums. Zbl 0739.34065Lapidus, Michel L.; Pomerance, Carl 56 1993 On distinguishing prime numbers from composite numbers. Zbl 0526.10004Adleman, Leonard M.; Pomerance, Carl; Rumely, Robert S. 49 1983 A search for Wieferich and Wilson primes. Zbl 0854.11002Crandall, Richard; Dilcher, Karl; Pomerance, Carl 45 1997 The pseudoprimes to \(25\cdot 10^9\). Zbl 0444.10007Pomerance, Carl; Selfridge, J. L.; Wagstaff, Samuel S. jun. 43 1980 Factoring integers with the number field sieve. Zbl 0806.11067Buhler, J. P.; Lenstra, H. W. jun.; Pomerance, Carl 35 1993 Popular values of Euler’s function. Zbl 0437.10001Pomerance, Carl 27 1980 On the normal number of prime factors of \(\phi(n)\). Zbl 0617.10037Erdős, Paul; Pomerance, Carl 26 1985 Carmichael’s lambda function. Zbl 0734.11047Erdős, Paul; Pomerance, Carl; Schmutz, Eric 24 1991 Counterexamples to the modified Weyl-Berry conjecture on fractal drums. Zbl 0858.58052Lapidus, Michel L.; Pomerance, Carl 23 1996 Period of the power generator and small values of Carmichael’s function. Zbl 1029.11043Friedlander, John B.; Pomerance, Carl; Shparlinski, Igor E. 20 2002 A rigorous time bound for factoring integers. Zbl 0770.11057Lenstra, H. W. jun.; Pomerance, Carl 20 1992 Unusually large gaps between consecutive primes. Zbl 0706.11052Maier, Helmut; Pomerance, Carl 20 1990 On the distribution of amicable numbers. Zbl 0349.10004Pomerance, Carl 20 1977 On primes recognizable in deterministic polynomial time. Zbl 0869.11102Konyagin, Sergei; Pomerance, Carl 19 1997 A note on the least prime in an arithmetic progression. Zbl 0436.10020Pomerance, Carl 19 1980 On the distribution of pseudoprimes. Zbl 0511.10002Pomerance, Carl 18 1981 On the binary expansions of algebraic numbers. Zbl 1076.11045Bailey, David H.; Borwein, Jonathan M.; Crandall, Richard E.; Pomerance, Carl 17 2004 Average case error estimates for the strong probable prime test. Zbl 0788.11059Damgård, Ivan; Landrock, Peter; Pomerance, Carl 16 1993 Error estimates for the Davenport-Heilbronn theorems. Zbl 1227.11114Belabas, Karim; Bhargava, Manjul; Pomerance, Carl 15 2010 On the periods of the linear congruential and power generators. Zbl 1080.11059Kurlberg, Pär; Pomerance, Carl 15 2005 View-obstruction problems. III. Zbl 0563.10026Cusick, T. W.; Pomerance, Carl 15 1984 On some problems of Mąkowski-Schinzel and Erdős concerning the arithmetical functions \(\varphi\) and \(\sigma\). Zbl 1027.11007Luca, 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 0707.58046Lapidus, Michel L.; Pomerance, Carl 14 1990 On numbers \(n\) dividing the \(n\)th term of a linear recurrence. Zbl 1262.11015Alba González, Juan José; Luca, Florian; Pomerance, Carl; Shparlinski, Igor E. 13 2012 Fast, rigorous factorization and discrete logarithm algorithm. Zbl 0659.10003Pomerance, Carl 13 1987 Analysis and comparison of some integer factoring algorithms. Zbl 0508.10004Pomerance, C. 13 1982 The role of smooth numbers in number theoretic algorithms. Zbl 0854.11047Pomerance, Carl 12 1995 On the normal behavior of the iterates of some arithmetic functions. Zbl 0721.11034Erdős, Paul; Granville, A.; Pomerance, C.; Spiro, C. 12 1990 Multiply perfect numbers, Mersenne primes, and effective computability. Zbl 0324.10001Pomerance, Carl 12 1977 Remarks on the Pólya-Vinogradov inequality. Zbl 1278.11080Pomerance, Carl 11 2011 Sieving by large integers and covering systems of congruences. Zbl 1210.11020Filaseta, Michael; Ford, Kevin; Konyagin, Sergei; Pomerance, Carl; Yu, Gang 11 2007 On the largest prime factor of a Mersenne number. Zbl 1077.11003Murata, Leo; Pomerance, Carl 11 2004 Combinatorial number theory. Zbl 0849.11001Pomerance, Carl; Sárközy, András 11 1995 Irreducible radical extensions and Euler-function chains. Zbl 1172.11029Luca, Florian; Pomerance, Carl 10 2007 The expected number of random elements to generate a finite Abelian group. Zbl 0980.20079Pomerance, Carl 10 2001 On the difficulty of finding reliable witnesses. Zbl 0828.11074Alford, W. R.; Granville, Andrew; Pomerance, Carl 10 1994 On divisors of sums of integers. III. Zbl 0668.10055Pomerance, Carl; Sárközy, A.; Stewart, C. L. 10 1988 On the largest prime factors of \(n\) and \(n+1\). Zbl 0379.10027Erdős, Paul; Pomerance, Carl 10 1978 Odd perfect numbers are divisible by at least seven distinct primes. Zbl 0247.10007Pomerance, Carl 10 1974 Divisors of the middle binomial coefficient. Zbl 1332.05005Pomerance, Carl 9 2015 Heuristics for class numbers of prime-power real cyclotomic fields. Zbl 1106.11039Buhler, Joe; Pomerance, Carl; Robertson, Leanne 9 2004 Smooth orders and cryptographic applications. Zbl 1058.11059Pomerance, Carl; Shparlinski, Igor E. 9 2002 Two contradictory conjectures concerning Carmichael numbers. Zbl 0991.11067Granville, Andrew; Pomerance, Carl 9 2002 A tale of two sieves. Zbl 1042.11529Pomerance, Carl 9 1996 A hyperelliptic smoothness test. I. Zbl 0808.11073Lenstra, H. W. jun.; Pila, J.; Pomerance, Carl 9 1993 On locally repeated values of certain arithmetic functions. II. Zbl 0609.10034Erdős, Paul; Pomerance, C.; Sárközy, A. 9 1987 The quadratic sieve factoring algorithm. Zbl 0596.10006Pomerance, Carl 9 1985 Recent developments in primality testing. Zbl 0476.10004Pomerance, Carl 9 1981 On the distribution in residue classes of integers with a fixed sum of digits. Zbl 1155.11345Mauduit, Christian; Pomerance, Carl; Sárközy, András 8 2005 On the problem of uniqueness for the maximum Stirling number(s) of the second kind. Zbl 1008.11006Canfield, E. Rodney; Pomerance, Carl 8 2002 The distribution of smooth numbers in arithmetic progressions. Zbl 0752.11036Balog, Antal; Pomerance, Carl 8 1992 On the number of distinct values of Euler’s \(\phi\)-function. Zbl 0638.10045Maier, Helmut; Pomerance, Carl 8 1988 On the distribution of amicable numbers. II. Zbl 0448.10007Pomerance, Carl 8 1981 On a problem of Arnold: the average multiplicative order of a given integer. Zbl 1282.11131Kurlberg, Pär; Pomerance, Carl 7 2013 On composite integers \(n\) for which \(\varphi(n)\mid n-1\). Zbl 1294.11005Luca, Florian; Pomerance, Carl 7 2011 Fixed points for discrete logarithms. Zbl 1260.11004Levin, Mariana; Pomerance, Carl; Soundararajan, K. 7 2010 Common values of the arithmetic functions \(\varphi\) and \(\sigma\). Zbl 1205.11010Ford, Kevin; Luca, Florian; Pomerance, Carl 7 2010 On the smallest pseudopower. Zbl 1242.11006Bourgain, Jean; Konyagin, Sergei V.; Pomerance, Carl; Shparlinski, Igor E. 7 2009 Products of ratios of consecutive integers. Zbl 1155.11343de la Bretèche, Régis; Pomerance, Carl; Tenenbaum, Gérald 7 2005 A hyperelliptic smoothness test. II. Zbl 0983.11072Lenstra, H. W. jun.; Pila, J.; Pomerance, Carl 7 2002 On the solutions to \(\varphi(n)=\varphi(n+k)\). Zbl 0937.11037Graham, S. W.; Holt, Jeffrey J.; Pomerance, Carl 7 1999 Reduction of huge, sparse matrices over finite fields via created catastrophes. Zbl 0771.65023Pomerance, Carl; Smith, J. W. 7 1992 The distribution of Lucas and elliptic pseudoprimes. Zbl 0744.11066Gordon, Daniel M.; Pomerance, Carl 7 1991 Two methods in elementary analytic number theory. Zbl 0683.10003Pomerance, Carl 7 1989 The generation of random numbers that are probably prime. Zbl 0669.10014Beauchemin, Pierre; Brassard, Gilles; Crépeau, Claude; Goutier, Claude; Pomerance, Carl 7 1988 On sums involving reciprocals of the largest prime factor of an integer. Zbl 0615.10055Erdős, Paul; Ivić, A.; Pomerance, C. 7 1986 On the number of false witnesses for a composite number. Zbl 0586.10003Erdős, Paul; Pomerance, Carl 7 1986 Implementation of the continued fraction integer factoring algorithm. Zbl 0556.10003Pomerance, Carl; Wagstaff, Samuel S. jun. 7 1983 Sets on which an entire function is determined by its range. Zbl 0473.30022Diamond, Harold G.; Pomerance, Carl; Rubel, Lee 7 1981 Primality testing with Gaussian periods. Zbl 1429.11221Lenstra, Hendrik W. jun.; Pomerance, Carl B. 6 2019 Some problems of Erdős on the sum-of-divisors function. Zbl 1365.11111Pollack, Paul; Pomerance, Carl 6 2016 Infinitude of elliptic Carmichael numbers. Zbl 1251.11004Ekstrom, Aaron; Pomerance, Carl; Thakur, Dinesh S. 6 2012 Prime numbers. A computational perspective. Zbl 0995.11072Crandall, Richard; Pomerance, Carl 6 1999 Rigorous discrete logarithm computations in finite fields via smooth polynomials. Zbl 0915.11063Bender, Renet Lovorn; Pomerance, Carl 6 1998 Euler’s function in residue classes. Zbl 0919.11006Dence, Thomas; Pomerance, Carl 6 1998 A pipeline architecture for factoring large integers with the quadratic sieve algorithm. Zbl 0644.10002Pomerance, Carl; Smith, J. W.; Tuler, Randy 6 1988 The smallest n-uniform hypergraph with positive discrepancy. Zbl 0629.05053Alon, N.; Kleitman, D. J.; Pomerance, C.; Saks, M.; Seymour, P. 6 1987 On the distribution of round numbers. Zbl 0565.10038Pomerance, 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 0719.11002Pomerance, Carl 6 1984 On composite \(n\) for which \(\varphi(n)\mid n-1\). II. Zbl 0328.10006Pomerance, Carl 6 1977 The second largest prime factor of an odd perfect number. Zbl 0307.10009Pomerance, Carl 6 1975 Explicit estimates for the distribution of numbers free of large prime factors. Zbl 1433.11109Lichtman, Jared D.; Pomerance, Carl 5 2018 On integers \(n\) for which \(X^n-1\) has a divisor of every degree. Zbl 1364.11143Pomerance, Carl; Thompson, Lola; Weingartner, Andreas 5 2016 On the counting function of irregular primes. Zbl 1356.11067Luca, Florian; Pizarro-Madariaga, Amalia; Pomerance, Carl 5 2015 On congruences of the form \(\sigma(n)\equiv a\pmod n\). Zbl 1271.11004Anavi, Aria; Pollack, Paul; Pomerance, Carl 5 2013 On Carmichael numbers in arithmetic progressions. Zbl 1208.11109Banks, William D.; Pomerance, Carl 5 2010 On the distribution of sociable numbers. Zbl 1241.11120Kobayashi, Mitsuo; Pollack, Paul; Pomerance, Carl 5 2009 On the average number of divisors of the Euler function. Zbl 1127.11065Luca, Florian; Pomerance, Carl 5 2007 The iterated Carmichael \(\lambda\)-function and the number of cycles of the power generator. Zbl 1109.11046Martin, Greg; Pomerance, Carl 5 2005 Timed fair exchange of standard signatures (extended abstract). Zbl 1274.94068Garay, Juan A.; Pomerance, Carl 5 2003 On generalizing Artin’s conjecture on primitive roots to composite moduli. Zbl 1022.11049Li, Shuguang; Pomerance, Carl 5 2003 On the number of divisors of \(n!\). Zbl 0858.11051Erdős, Paul; Graham, S. W.; Ivić, Aleksandar; Pomerance, Carl 5 1996 On the least prime in certain arithmetic progression. Zbl 0658.10049Granville, Andrew; Pomerance, Carl 5 1990 Very short primality proofs. Zbl 0608.10002Pomerance, Carl 5 1987 On the longest simple path in the divisor graph. Zbl 0546.05038Pomerance, Carl 5 1983 Proof of D. J. Newman’s coprime mapping conjecture. Zbl 0442.10003Pomerance, Carl; Selfridge, J. L. 5 1980 The prime number graph. Zbl 0396.10002Pomerance, Carl 5 1979 Counting elliptic curves with an isogeny of degree three. Zbl 07177262Pizzo, Maggie; Pomerance, Carl; Voight, John 1 2020 Primality testing with Gaussian periods. Zbl 1429.11221Lenstra, Hendrik W. jun.; Pomerance, Carl B. 6 2019 The reciprocal sum of the amicable numbers. Zbl 1429.11009Nguyen, Hanh My; Pomerance, Carl 4 2019 The Erdős conjecture for primitive sets. Zbl 07046192Lichtman, Jared Duker; Pomerance, Carl 3 2019 Symmetric primes revisited. Zbl 07133445Banks, William; Pollack, Paul; Pomerance, Carl 1 2019 Proof of the Sheldon conjecture. Zbl 07109913Pomerance, Carl; Spicer, Chris 1 2019 Primes in prime number races. Zbl 07102537Lichtman, Jared Duker; Martin, Greg; Pomerance, Carl 1 2019 Explicit estimates for the distribution of numbers free of large prime factors. Zbl 1433.11109Lichtman, Jared D.; Pomerance, Carl 5 2018 Divisor-sum fibers. Zbl 1410.11115Pollack, Paul; Pomerance, Carl; Thompson, Lola 4 2018 Density of singular pairs of integers. Zbl 1430.11134Nedela, Roman; Pomerance, Carl 1 2018 The first function and its iterates. Zbl 1431.11010Pomerance, Carl 1 2018 The aliquot constant, after Bosma and Kane. Zbl 1445.11102Pomerance, Carl 1 2018 Numbers divisible by a large shifted prime and large torsion subgroups of CM elliptic curves. Zbl 1405.11123McNew, Nathan; Pollack, Paul; Pomerance, Carl 3 2017 Local behavior of the composition of the aliquot and co-totient functions. Zbl 1421.11076Luca, Florian; Pomerance, Carl 1 2017 Squarefree smooth numbers and Euclidean prime generators. Zbl 1437.11007Booker, Andrew R.; Pomerance, Carl 1 2017 Triangles with prime hypotenuse. Zbl 1426.11095Chow, Sam; Pomerance, Carl 1 2017 Some problems of Erdős on the sum-of-divisors function. Zbl 1365.11111Pollack, Paul; Pomerance, Carl 6 2016 On integers \(n\) for which \(X^n-1\) has a divisor of every degree. Zbl 1364.11143Pomerance, Carl; Thompson, Lola; Weingartner, Andreas 5 2016 Generating random factored Gaussian integers, easily. Zbl 1327.65009Lebowitz-Lockard, Noah; Pomerance, Carl 1 2016 Divisors of the middle binomial coefficient. Zbl 1332.05005Pomerance, Carl 9 2015 On the counting function of irregular primes. Zbl 1356.11067Luca, Florian; Pizarro-Madariaga, Amalia; Pomerance, Carl 5 2015 Sierpiński and Carmichael numbers. Zbl 1325.11010Banks, William; Finch, Carrie; Luca, Florian; Pomerance, Carl; Stănică, Pantelimon 3 2015 On amicable numbers. Zbl 1395.11017Pomerance, Carl 2 2015 Analytic number theory. In honor of Helmut Maier’s 60th birthday. Zbl 1336.11002Pomerance, Carl (ed.); Rassias, Michael Th. (ed.) 2 2015 The range of the sum-of-proper-divisors function. Zbl 1394.11007Luca, Florian; Pomerance, Carl 2 2015 A note on square totients. Zbl 1331.11085Freiberg, Tristan; Pomerance, Carl 1 2015 The image of Carmichael’s \(\lambda\)-function. Zbl 1322.11104Ford, Kevin; Luca, Florian; Pomerance, Carl 3 2014 Variant of a theorem of Erdős on the sum-of-proper-divisors function. Zbl 1297.11006Pomerance, Carl; Yang, Hee-Sung 3 2014 Square values of Euler’s function. Zbl 1297.11125Pollack, Paul; Pomerance, Carl 2 2014 On the local behavior of the order of appearance in the Fibonacci sequence. Zbl 1387.11016Luca, Florian; Pomerance, Carl 1 2014 On the range of Carmichael’s universal-exponent function. Zbl 1292.11109Luca, Florian; Pomerance, Carl 1 2014 On a problem of Arnold: the average multiplicative order of a given integer. Zbl 1282.11131Kurlberg, Pär; Pomerance, Carl 7 2013 On congruences of the form \(\sigma(n)\equiv a\pmod n\). Zbl 1271.11004Anavi, Aria; Pollack, Paul; Pomerance, Carl 5 2013 On balanced subgroups of the multiplicative group. Zbl 1332.11089Pomerance, Carl; Ulmer, Douglas 4 2013 On the distribution of some integers related to perfect and amicable numbers. Zbl 1285.11009Pollack, Paul; Pomerance, Carl 3 2013 On numbers \(n\) dividing the \(n\)th term of a linear recurrence. Zbl 1262.11015Alba González, Juan José; Luca, Florian; Pomerance, Carl; Shparlinski, Igor E. 13 2012 Infinitude of elliptic Carmichael numbers. Zbl 1251.11004Ekstrom, Aaron; Pomerance, Carl; Thakur, Dinesh S. 6 2012 Prime-perfect numbers. Zbl 1271.11006Pollack, Paul; Pomerance, Carl 3 2012 The average order of elements in the multiplicative group of a finite field. Zbl 1285.11022Hu, Yilan; Pomerance, Carl 1 2012 Product-free sets with high density. Zbl 1357.11028Kurlberg, Pär; Lagarias, Jeffrey C.; Pomerance, Carl 1 2012 Remarks on the Pólya-Vinogradov inequality. Zbl 1278.11080Pomerance, Carl 11 2011 On composite integers \(n\) for which \(\varphi(n)\mid n-1\). Zbl 1294.11005Luca, Florian; Pomerance, Carl 7 2011 Primitive sets with large counting functions. Zbl 1249.11016Martin, Greg; Pomerance, Carl 2 2011 Fibonacci integers. Zbl 1225.11022Luca, Florian; Pomerance, Carl; Wagner, Stephan 1 2011 Error estimates for the Davenport-Heilbronn theorems. Zbl 1227.11114Belabas, Karim; Bhargava, Manjul; Pomerance, Carl 15 2010 Fixed points for discrete logarithms. Zbl 1260.11004Levin, Mariana; Pomerance, Carl; Soundararajan, K. 7 2010 Common values of the arithmetic functions \(\varphi\) and \(\sigma\). Zbl 1205.11010Ford, Kevin; Luca, Florian; Pomerance, Carl 7 2010 On Carmichael numbers in arithmetic progressions. Zbl 1208.11109Banks, William D.; Pomerance, Carl 5 2010 Primality testing: variations on a theme of Lucas. Zbl 1203.11083Pomerance, Carl 4 2010 On the radical of a perfect number. Zbl 1230.11008Luca, Florian; Pomerance, Carl 3 2010 On the distribution of pseudopowers. Zbl 1197.11004Konyagin, Sergei V.; Pomerance, Carl; Shparlinski, Igor E. 3 2010 On the asymptotic effectiveness of Weil descent attacks. Zbl 1252.94080Karabina, Koray; Menezes, Alfred; Pomerance, Carl; Shparlinski, Igor E. 1 2010 Rank statistics for a family of elliptic curves over a function field. Zbl 1200.14060Pomerance, Carl; Shparlinski, Igor E. 1 2010 On the smallest pseudopower. Zbl 1242.11006Bourgain, Jean; Konyagin, Sergei V.; Pomerance, Carl; Shparlinski, Igor E. 7 2009 On the distribution of sociable numbers. Zbl 1241.11120Kobayashi, Mitsuo; Pollack, Paul; Pomerance, Carl 5 2009 A remark on Giuga’s conjecture and Lehmer’s totient problem. Zbl 1219.11003Banks, William D.; Nevans, C. Wesley; Pomerance, Carl 3 2009 On Giuga numbers. Zbl 1231.11115Luca, Florian; Pomerance, Carl; Shparlinski, Igor 2 2009 On the range of the iterated Euler function. Zbl 1184.11043Luca, Florian; Pomerance, Carl 2 2009 On pseudosquares and pseudopowers. Zbl 1184.11026Pomerance, Carl; Shparlinski, Igor E. 1 2009 Sets with prescribed arithmetic densities. Zbl 1212.11018Luca, Florian; Pomerance, Carl; Porubský, Štefan 4 2008 On the proportion of numbers coprime to a given integer. Zbl 1175.11055Erdős, Paul; Luca, Florian; Pomerance, Carl 4 2008 Smooth numbers and the quadratic sieve. Zbl 1188.11065Pomerance, Carl 3 2008 Elementary thoughts on discrete logarithms. Zbl 1188.11070Pomerance, Carl 2 2008 Sieving by large integers and covering systems of congruences. Zbl 1210.11020Filaseta, Michael; Ford, Kevin; Konyagin, Sergei; Pomerance, Carl; Yu, Gang 11 2007 Irreducible radical extensions and Euler-function chains. Zbl 1172.11029Luca, Florian; Pomerance, Carl 10 2007 On the average number of divisors of the Euler function. Zbl 1127.11065Luca, Florian; Pomerance, Carl 5 2007 Maximal height of divisors of \(x^n-1\). Zbl 1211.11108Pomerance, Carl; Ryan, Nathan C. 4 2007 Prime numbers. A computational perspective. 2nd ed. Zbl 1088.11001Crandall, Richard; Pomerance, Carl 123 2005 On the periods of the linear congruential and power generators. Zbl 1080.11059Kurlberg, Pär; Pomerance, Carl 15 2005 On the distribution in residue classes of integers with a fixed sum of digits. Zbl 1155.11345Mauduit, Christian; Pomerance, Carl; Sárközy, András 8 2005 Products of ratios of consecutive integers. Zbl 1155.11343de la Bretèche, Régis; Pomerance, Carl; Tenenbaum, Gérald 7 2005 The iterated Carmichael \(\lambda\)-function and the number of cycles of the power generator. Zbl 1109.11046Martin, Greg; Pomerance, Carl 5 2005 On the binary expansions of algebraic numbers. Zbl 1076.11045Bailey, David H.; Borwein, Jonathan M.; Crandall, Richard E.; Pomerance, Carl 17 2004 On the largest prime factor of a Mersenne number. Zbl 1077.11003Murata, Leo; Pomerance, Carl 11 2004 Heuristics for class numbers of prime-power real cyclotomic fields. Zbl 1106.11039Buhler, Joe; Pomerance, Carl; Robertson, Leanne 9 2004 Multiplicative structure of values of the Euler function. Zbl 1099.11055Banks, William D.; Friedlander, John B.; Pomerance, Carl; Shparlinski, Igor E. 4 2004 Timed fair exchange of standard signatures (extended abstract). Zbl 1274.94068Garay, Juan A.; Pomerance, Carl 5 2003 On generalizing Artin’s conjecture on primitive roots to composite moduli. Zbl 1022.11049Li, Shuguang; Pomerance, Carl 5 2003 Period of the power generator and small values of Carmichael’s function. Zbl 1029.11043Friedlander, 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 1027.11007Luca, Florian; Pomerance, Carl 14 2002 Smooth orders and cryptographic applications. Zbl 1058.11059Pomerance, Carl; Shparlinski, Igor E. 9 2002 Two contradictory conjectures concerning Carmichael numbers. Zbl 0991.11067Granville, Andrew; Pomerance, Carl 9 2002 On the problem of uniqueness for the maximum Stirling number(s) of the second kind. Zbl 1008.11006Canfield, E. Rodney; Pomerance, Carl 8 2002 A hyperelliptic smoothness test. II. Zbl 0983.11072Lenstra, H. W. jun.; Pila, J.; Pomerance, Carl 7 2002 Ruth-Aaron numbers revisited. Zbl 1051.11052Pomerance, C. 2 2002 Primitive roots: a survey. Zbl 1132.11358Li, Shuguang; Pomerance, Carl 1 2002 Primitive roots: a survey. Zbl 1175.11057Li, Shuguang; Pomerance, Carl 1 2002 The expected number of random elements to generate a finite Abelian group. Zbl 0980.20079Pomerance, Carl 10 2001 Small values of the Carmichael function and cryptographic applications. Zbl 0996.11075Friedlander, John B.; Pomerance, Carl; Shparlinski, Igor E. 1 2001 On the solutions to \(\varphi(n)=\varphi(n+k)\). Zbl 0937.11037Graham, S. W.; Holt, Jeffrey J.; Pomerance, Carl 7 1999 Prime numbers. A computational perspective. Zbl 0995.11072Crandall, Richard; Pomerance, Carl 6 1999 Residue classes free of values of Euler’s function. Zbl 0931.11037Ford, Kevin; Konyagin, Sergei; Pomerance, Carl 4 1999 Rigorous discrete logarithm computations in finite fields via smooth polynomials. Zbl 0915.11063Bender, Renet Lovorn; Pomerance, Carl 6 1998 Euler’s function in residue classes. Zbl 0919.11006Dence, Thomas; Pomerance, Carl 6 1998 A search for Wieferich and Wilson primes. Zbl 0854.11002Crandall, Richard; Dilcher, Karl; Pomerance, Carl 45 1997 On primes recognizable in deterministic polynomial time. Zbl 0869.11102Konyagin, Sergei; Pomerance, Carl 19 1997 Automaticity. II: Descriptional complexity in the unary case. Zbl 0959.11015Pomerance, Carl; Robson, John Michael; Shallit, Jeffrey 4 1997 Counterexamples to the modified Weyl-Berry conjecture on fractal drums. Zbl 0858.58052Lapidus, Michel L.; Pomerance, Carl 23 1996 A tale of two sieves. Zbl 1042.11529Pomerance, Carl 9 1996 On the number of divisors of \(n!\). Zbl 0858.11051Erdős, Paul; Graham, S. W.; Ivić, Aleksandar; Pomerance, Carl 5 1996 ...and 89 more Documents all cited Publications top 5 cited Publications 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 all top 5 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) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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