Edit Profile (opens in new tab) Pomerance, Carl Bernard Compute Distance To: Compute 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 all top 5 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 all top 5 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 all top 5 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) Publications by Year all cited Publications top 5 cited Publications 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 1088.11001Crandall, Richard; Pomerance, Carl 125 2005 On a problem of Oppenheim concerning ”Factorisatio Numerorum”. Zbl 0513.10043Canfield, E. R.; Erdős, Paul; Pomerance, Carl 107 1983 There are infinitely many Carmichael numbers. Zbl 0816.11005Alford, W. R.; Granville, Andrew; Pomerance, Carl 106 1994 The Riemann zeta-function and the one-dimensional Weyl-Berry conjecture for fractal drums. Zbl 0739.34065Lapidus, Michel L.; Pomerance, Carl 59 1993 On distinguishing prime numbers from composite numbers. Zbl 0526.10004Adleman, Leonard M.; Pomerance, Carl; Rumely, Robert S. 53 1983 The pseudoprimes to \(25\cdot 10^9\). Zbl 0444.10007Pomerance, Carl; Selfridge, J. L.; Wagstaff, Samuel S. jun. 49 1980 A search for Wieferich and Wilson primes. Zbl 0854.11002Crandall, Richard; Dilcher, Karl; Pomerance, Carl 47 1997 Factoring integers with the number field sieve. Zbl 0806.11067Buhler, J. P.; Lenstra, H. W. jun.; Pomerance, Carl 36 1993 Popular values of Euler’s function. Zbl 0437.10001Pomerance, Carl 29 1980 Carmichael’s lambda function. Zbl 0734.11047Erdős, Paul; Pomerance, Carl; Schmutz, Eric 27 1991 On the normal number of prime factors of \(\phi(n)\). Zbl 0617.10037Erdős, Paul; Pomerance, Carl 26 1985 Counterexamples to the modified Weyl-Berry conjecture on fractal drums. Zbl 0858.58052Lapidus, Michel L.; Pomerance, Carl 25 1996 On the distribution of amicable numbers. Zbl 0349.10004Pomerance, Carl 22 1977 A rigorous time bound for factoring integers. Zbl 0770.11057Lenstra, H. W. jun.; Pomerance, Carl 21 1992 Unusually large gaps between consecutive primes. Zbl 0706.11052Maier, Helmut; Pomerance, Carl 21 1990 On the distribution of pseudoprimes. Zbl 0511.10002Pomerance, Carl 20 1981 A note on the least prime in an arithmetic progression. Zbl 0436.10020Pomerance, Carl 20 1980 Period of the power generator and small values of Carmichael’s function. Zbl 1029.11043Friedlander, John B.; Pomerance, Carl; Shparlinski, Igor E. 19 2002 On primes recognizable in deterministic polynomial time. Zbl 0869.11102Konyagin, Sergei; Pomerance, Carl 19 1997 On the binary expansions of algebraic numbers. Zbl 1076.11045Bailey, David H.; Borwein, Jonathan M.; Crandall, Richard E.; Pomerance, Carl 18 2004 View-obstruction problems. III. Zbl 0563.10026Cusick, T. W.; Pomerance, Carl 17 1984 Average case error estimates for the strong probable prime test. Zbl 0788.11059Damgård, Ivan; Landrock, Peter; Pomerance, Carl 16 1993 Sieving by large integers and covering systems of congruences. Zbl 1210.11020Filaseta, Michael; Ford, Kevin; Konyagin, Sergei; Pomerance, Carl; Yu, Gang 16 2007 Error estimates for the Davenport-Heilbronn theorems. Zbl 1227.11114Belabas, Karim; Bhargava, Manjul; Pomerance, Carl 15 2010 Remarks on the Pólya-Vinogradov inequality. Zbl 1278.11080Pomerance, Carl 14 2011 Analysis and comparison of some integer factoring algorithms. Zbl 0508.10004Pomerance, C. 14 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 0707.58046Lapidus, Michel L.; Pomerance, Carl 14 1990 On some problems of Mąkowski-Schinzel and Erdős concerning the arithmetical functions \(\varphi\) and \(\sigma\). Zbl 1027.11007Luca, Florian; Pomerance, Carl 14 2002 On the periods of the linear congruential and power generators. Zbl 1080.11059Kurlberg, Pär; Pomerance, Carl 14 2005 The role of smooth numbers in number theoretic algorithms. Zbl 0854.11047Pomerance, Carl 13 1995 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 On the largest prime factors of \(n\) and \(n+1\). Zbl 0379.10027Erdős, Paul; Pomerance, Carl 12 1978 Multiply perfect numbers, Mersenne primes, and effective computability. Zbl 0324.10001Pomerance, Carl 12 1977 A tale of two sieves. Zbl 1042.11529Pomerance, Carl 12 1996 The expected number of random elements to generate a finite Abelian group. Zbl 0980.20079Pomerance, Carl 12 2001 On locally repeated values of certain arithmetic functions. II. Zbl 0609.10034Erdős, Paul; Pomerance, C.; Sárközy, A. 11 1987 On the difficulty of finding reliable witnesses. Zbl 0828.11074Alford, W. R.; Granville, Andrew; Pomerance, Carl 11 1994 Combinatorial number theory. Zbl 0849.11001Pomerance, Carl; Sárközy, András 11 1995 Fast, rigorous factorization and discrete logarithm algorithm. Zbl 0659.10003Pomerance, Carl 11 1987 Two contradictory conjectures concerning Carmichael numbers. Zbl 0991.11067Granville, Andrew; Pomerance, Carl 11 2002 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 11 2004 Prime numbers. A computational perspective. Zbl 0995.11072Crandall, Richard; Pomerance, Carl 11 1999 Recent developments in primality testing. Zbl 0476.10004Pomerance, Carl 11 1981 The quadratic sieve factoring algorithm. Zbl 0596.10006Pomerance, Carl 10 1985 Odd perfect numbers are divisible by at least seven distinct primes. Zbl 0247.10007Pomerance, Carl 10 1974 Smooth orders and cryptographic applications. Zbl 1058.11059Pomerance, Carl; Shparlinski, Igor E. 10 2002 Divisors of the middle binomial coefficient. Zbl 1332.05005Pomerance, Carl 10 2015 On the number of distinct values of Euler’s \(\varphi\)-function. Zbl 0638.10045Maier, Helmut; Pomerance, Carl 9 1988 Implementation of the continued fraction integer factoring algorithm. Zbl 0556.10003Pomerance, Carl; Wagstaff, Samuel S. jun. 9 1983 A hyperelliptic smoothness test. I. Zbl 0808.11073Lenstra, H. W. jun.; Pila, J.; Pomerance, Carl 9 1993 Irreducible radical extensions and Euler-function chains. Zbl 1172.11029Luca, Florian; Pomerance, Carl 9 2007 On Carmichael numbers in arithmetic progressions. Zbl 1208.11109Banks, William D.; Pomerance, Carl 9 2010 On divisors of sums of integers. III. Zbl 0668.10055Pomerance, Carl; Sárközy, A.; Stewart, C. L. 9 1988 On the problem of uniqueness for the maximum Stirling number(s) of the second kind. Zbl 1008.11006Canfield, E. Rodney; Pomerance, Carl 9 2002 On the distribution in residue classes of integers with a fixed sum of digits. Zbl 1155.11345Mauduit, Christian; Pomerance, Carl; Sárközy, András 9 2005 The distribution of Lucas and elliptic pseudoprimes. Zbl 0744.11066Gordon, Daniel M.; Pomerance, Carl 8 1991 The distribution of smooth numbers in arithmetic progressions. Zbl 0752.11036Balog, Antal; Pomerance, Carl 8 1992 Primality testing with Gaussian periods. Zbl 1429.11221Lenstra, Hendrik W. jun.; Pomerance, Carl B. 8 2019 On the number of false witnesses for a composite number. Zbl 0586.10003Erdős, Paul; Pomerance, Carl 8 1986 Fixed points for discrete logarithms. Zbl 1260.11004Levin, Mariana; Pomerance, Carl; Soundararajan, K. 8 2010 Common values of the arithmetic functions \(\varphi\) and \(\sigma\). Zbl 1205.11010Ford, Kevin; Luca, Florian; Pomerance, Carl 8 2010 On the normal behavior of the iterates of some arithmetic functions. Zbl 0721.11034Erdős, Paul; Granville, A.; Pomerance, C.; Spiro, C. 8 1990 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 8 2013 Reduction of huge, sparse matrices over finite fields via created catastrophes. Zbl 0771.65023Pomerance, Carl; Smith, J. W. 7 1992 On sums involving reciprocals of the largest prime factor of an integer. Zbl 0615.10055Erdős, Paul; Ivić, A.; Pomerance, C. 7 1986 The smallest n-uniform hypergraph with positive discrepancy. Zbl 0629.05053Alon, N.; Kleitman, D. J.; Pomerance, C.; Saks, M.; Seymour, P. 7 1987 On the distribution of round numbers. Zbl 0565.10038Pomerance, Carl 7 1985 On the smallest pseudopower. Zbl 1242.11006Bourgain, Jean; Konyagin, Sergei V.; Pomerance, Carl; Shparlinski, Igor E. 7 2009 The generation of random numbers that are probably prime. Zbl 0669.10014Beauchemin, Pierre; Brassard, Gilles; Crépeau, Claude; Goutier, Claude; Pomerance, Carl 7 1988 A hyperelliptic smoothness test. II. Zbl 0983.11072Lenstra, H. W. jun.; Pila, J.; Pomerance, Carl 7 2002 Products of ratios of consecutive integers. Zbl 1155.11343de la Bretèche, Régis; Pomerance, Carl; Tenenbaum, Gérald 7 2005 On the solutions to \(\varphi(n)=\varphi(n+k)\). Zbl 0937.11037Graham, S. W.; Holt, Jeffrey J.; Pomerance, Carl 7 1999 Proof of D. J. Newman’s coprime mapping conjecture. Zbl 0442.10003Pomerance, Carl; Selfridge, J. L. 7 1980 Sets on which an entire function is determined by its range. Zbl 0473.30022Diamond, Harold G.; Pomerance, Carl; Rubel, Lee 7 1981 Infinitude of elliptic Carmichael numbers. Zbl 1251.11004Ekstrom, Aaron; Pomerance, Carl; Thakur, Dinesh S. 7 2012 On composite integers \(n\) for which \(\varphi(n)\mid n-1\). Zbl 1294.11005Luca, Florian; Pomerance, Carl 7 2011 Some problems of Erdős on the sum-of-divisors function. Zbl 1365.11111Pollack, Paul; Pomerance, Carl 7 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 0719.11002Pomerance, Carl 6 1984 On locally repeated values of certain arithmetic functions. III. Zbl 0631.10029Erdős, Paul; Pomerance, Carl; Sárközy, András 6 1987 A pipeline architecture for factoring large integers with the quadratic sieve algorithm. Zbl 0644.10002Pomerance, Carl; Smith, J. W.; Tuler, Randy 6 1988 Some new results on odd perfect numbers. Zbl 0295.10005Dandapat, G. G.; Hunsucker, J. L.; Pomerance, Carl 6 1975 The second largest prime factor of an odd perfect number. Zbl 0307.10009Pomerance, Carl 6 1975 On the least prime in certain arithmetic progression. Zbl 0658.10049Granville, Andrew; Pomerance, Carl 6 1990 Two methods in elementary analytic number theory. Zbl 0683.10003Pomerance, Carl 6 1989 Euler’s function in residue classes. Zbl 0919.11006Dence, Thomas; Pomerance, Carl 6 1998 Rigorous discrete logarithm computations in finite fields via smooth polynomials. Zbl 0915.11063Bender, Renet Lovorn; Pomerance, Carl 6 1998 On the counting function of irregular primes. Zbl 1356.11067Luca, Florian; Pizarro-Madariaga, Amalia; Pomerance, Carl 6 2015 On integers \(n\) for which \(X^n-1\) has a divisor of every degree. Zbl 1364.11143Pomerance, Carl; Thompson, Lola; Weingartner, Andreas 6 2016 On the average number of divisors of the Euler function. Zbl 1127.11065Luca, Florian; Pomerance, Carl 5 2007 Very short primality proofs. Zbl 0608.10002Pomerance, Carl 5 1987 Estimates for certain sums involving the largest prime factor of an integer. Zbl 0546.10037Ivić, A.; Pomerance, C. 5 1984 The Erdős conjecture for primitive sets. Zbl 1481.11026Lichtman, Jared Duker; Pomerance, Carl 5 2019 On generalizing Artin’s conjecture on primitive roots to composite moduli. Zbl 1022.11049Li, Shuguang; Pomerance, Carl 5 2003 Sets with prescribed arithmetic densities. Zbl 1212.11018Luca, Florian; Pomerance, Carl; Porubský, Štefan 5 2008 Timed fair exchange of standard signatures (extended abstract). Zbl 1274.94068Garay, Juan A.; Pomerance, Carl 5 2003 On the radical of a perfect number. Zbl 1230.11008Luca, Florian; Pomerance, Carl 5 2010 Primality testing: variations on a theme of Lucas. Zbl 1203.11083Pomerance, Carl 5 2010 On the number of divisors of \(n!\). Zbl 0858.11051Erdős, Paul; Graham, S. W.; Ivić, Aleksandar; Pomerance, Carl 5 1996 On primes and practical numbers. Zbl 07490456Pomerance, Carl; Weingartner, Andreas 1 2022 Elliptic curves with Galois-stable cyclic subgroups of order 4. Zbl 1478.11084Pomerance, Carl; Schaefer, Edward F. 1 2021 A note on Carmichael numbers in residue classes. Zbl 07497816Pomerance, Carl 1 2021 Counting elliptic curves with an isogeny of degree three. Zbl 1483.11118Pizzo, Maggie; Pomerance, Carl; Voight, John 2 2020 Phi, primorials, and Poisson. Zbl 1453.11123Pollack, Paul; Pomerance, Carl 1 2020 Progress towards a nonintegrality conjecture. Zbl 1465.05007Laishram, Shanta; López-Aguayo, Daniel; Pomerance, Carl; Thongjunthug, Thotsaphon 1 2020 Primality testing with Gaussian periods. Zbl 1429.11221Lenstra, Hendrik W. jun.; Pomerance, Carl B. 8 2019 The Erdős conjecture for primitive sets. Zbl 1481.11026Lichtman, Jared Duker; Pomerance, Carl 5 2019 The reciprocal sum of the amicable numbers. Zbl 1429.11009Nguyen, Hanh My; Pomerance, Carl 5 2019 Primes in prime number races. Zbl 1473.11177Lichtman, Jared Duker; Martin, Greg; Pomerance, Carl 2 2019 Proof of the Sheldon conjecture. Zbl 1473.11018Pomerance, Carl; Spicer, Chris 1 2019 Symmetric primes revisited. Zbl 1462.11070Banks, William; Pollack, Paul; Pomerance, Carl 1 2019 Counting integers with a smooth totient. Zbl 1475.11177Banks, W. D.; Friedlander, J. B.; Pomerance, C.; Shparlinski, I. E. 1 2019 Divisor-sum fibers. Zbl 1410.11115Pollack, Paul; Pomerance, Carl; Thompson, Lola 5 2018 Explicit estimates for the distribution of numbers free of large prime factors. Zbl 1433.11109Lichtman, Jared D.; Pomerance, Carl 5 2018 The first function and its iterates. Zbl 1431.11010Pomerance, Carl 2 2018 Density of singular pairs of integers. Zbl 1430.11134Nedela, Roman; Pomerance, Carl 2 2018 The aliquot constant, after Bosma and Kane. Zbl 1445.11102Pomerance, Carl 1 2018 Connected components of the graph generated by power maps in prime finite fields. Zbl 1441.05108Pomerance, Carl; Shparlinksi, Igor E. 1 2018 Improved error bounds for the Fermat primality test on random inputs. Zbl 1441.11302Lichtman, Jared Duker; Pomerance, Carl 1 2018 Squarefree smooth numbers and Euclidean prime generators. Zbl 1437.11007Booker, Andrew R.; Pomerance, Carl 3 2017 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 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 7 2016 On integers \(n\) for which \(X^n-1\) has a divisor of every degree. Zbl 1364.11143Pomerance, Carl; Thompson, Lola; Weingartner, Andreas 6 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 10 2015 On the counting function of irregular primes. Zbl 1356.11067Luca, Florian; Pizarro-Madariaga, Amalia; Pomerance, Carl 6 2015 The range of the sum-of-proper-divisors function. Zbl 1394.11007Luca, Florian; Pomerance, Carl 3 2015 Sierpiński and Carmichael numbers. Zbl 1325.11010Banks, William; Finch, Carrie; Luca, Florian; Pomerance, Carl; Stănică, Pantelimon 2 2015 Analytic number theory. In honor of Helmut Maier’s 60th birthday. Zbl 1336.11002 2 2015 On amicable numbers. Zbl 1395.11017Pomerance, 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 8 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 Sets of monotonicity for Euler’s totient function. Zbl 1348.11003Pollack, Paul; Pomerance, Carl; Treviño, Enrique 1 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. 7 2012 Prime-perfect numbers. Zbl 1271.11006Pollack, Paul; Pomerance, Carl 3 2012 Product-free sets with high density. Zbl 1357.11028Kurlberg, Pär; Lagarias, Jeffrey C.; Pomerance, Carl 1 2012 The average order of elements in the multiplicative group of a finite field. Zbl 1285.11022Hu, Yilan; Pomerance, Carl 1 2012 Remarks on the Pólya-Vinogradov inequality. Zbl 1278.11080Pomerance, Carl 14 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 On Carmichael numbers in arithmetic progressions. Zbl 1208.11109Banks, William D.; Pomerance, Carl 9 2010 Fixed points for discrete logarithms. Zbl 1260.11004Levin, Mariana; Pomerance, Carl; Soundararajan, K. 8 2010 Common values of the arithmetic functions \(\varphi\) and \(\sigma\). Zbl 1205.11010Ford, Kevin; Luca, Florian; Pomerance, Carl 8 2010 On the radical of a perfect number. Zbl 1230.11008Luca, Florian; Pomerance, Carl 5 2010 Primality testing: variations on a theme of Lucas. Zbl 1203.11083Pomerance, Carl 5 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 the range of the iterated Euler function. Zbl 1184.11043Luca, Florian; Pomerance, Carl 2 2009 On Giuga numbers. Zbl 1231.11115Luca, Florian; Pomerance, Carl; Shparlinski, Igor 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 5 2008 On the proportion of numbers coprime to a given integer. Zbl 1175.11055Erdős, Paul; Luca, Florian; Pomerance, Carl 5 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 16 2007 Irreducible radical extensions and Euler-function chains. Zbl 1172.11029Luca, Florian; Pomerance, Carl 9 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 125 2005 On the periods of the linear congruential and power generators. Zbl 1080.11059Kurlberg, Pär; Pomerance, Carl 14 2005 On the distribution in residue classes of integers with a fixed sum of digits. Zbl 1155.11345Mauduit, Christian; Pomerance, Carl; Sárközy, András 9 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 18 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 11 2004 Multiplicative structure of values of the Euler function. Zbl 1099.11055Banks, William D.; Friedlander, John B.; Pomerance, Carl; Shparlinski, Igor E. 4 2004 On generalizing Artin’s conjecture on primitive roots to composite moduli. Zbl 1022.11049Li, Shuguang; Pomerance, Carl 5 2003 Timed fair exchange of standard signatures (extended abstract). Zbl 1274.94068Garay, Juan A.; 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. 19 2002 On some problems of Mąkowski-Schinzel and Erdős concerning the arithmetical functions \(\varphi\) and \(\sigma\). Zbl 1027.11007Luca, Florian; Pomerance, Carl 14 2002 Two contradictory conjectures concerning Carmichael numbers. Zbl 0991.11067Granville, Andrew; Pomerance, Carl 11 2002 Smooth orders and cryptographic applications. Zbl 1058.11059Pomerance, Carl; Shparlinski, Igor E. 10 2002 On the problem of uniqueness for the maximum Stirling number(s) of the second kind. Zbl 1008.11006Canfield, E. Rodney; Pomerance, Carl 9 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 1175.11057Li, Shuguang; Pomerance, Carl 1 2002 Primitive roots: a survey. Zbl 1132.11358Li, Shuguang; Pomerance, Carl 1 2002 The expected number of random elements to generate a finite Abelian group. Zbl 0980.20079Pomerance, Carl 12 2001 Small values of the Carmichael function and cryptographic applications. Zbl 0996.11075Friedlander, John B.; Pomerance, Carl; Shparlinski, Igor E. 1 2001 Prime numbers. A computational perspective. Zbl 0995.11072Crandall, Richard; Pomerance, Carl 11 1999 On the solutions to \(\varphi(n)=\varphi(n+k)\). Zbl 0937.11037Graham, S. W.; Holt, Jeffrey J.; Pomerance, Carl 7 1999 ...and 99 more Documents all cited Publications top 5 cited Publications 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 all top 5 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) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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