Edit Profile (opens in new tab) Williams, Hugh Cowie Co-Author Distance Author ID: williams.hugh-cowie Published as: Williams, H. C.; Williams, Hugh C.; Williams, Hugh more...less Homepage: http://people.ucalgary.ca/~hwilliam/ External Links: MGP · Wikidata · dblp · GND · IdRef Documents Indexed: 218 Publications since 1965, including 4 Books 13 Contributions as Editor · 1 Further Contribution Biographic References: 2 Publications Co-Authors: 79 Co-Authors with 173 Joint Publications 1,516 Co-Co-Authors all top 5 Co-Authors 58 single-authored 29 Mollin, Richard Anthony 14 Buchmann, Johannes A. 13 Jacobson, Michael John jun. 11 Roettger, Eric L. 11 Zarnke, C. R. 10 Scheidler, Renate 6 Guy, Richard Kenneth 5 Fung, Gilbert W. 5 Lukes, Richard F. 5 Shanks, Daniel C. 5 van der Poorten, Alfred J. 4 Beach, B. D. 4 Cormack, Gordon V. 4 Dueck, Gerhard W. 4 Patterson, C. D. 4 Stanton, Ralph Gordon 4 Stein, Andreas 4 Stephens, Alisa J. 3 Hartnell, Bert L. 3 Judd, J. S. 3 Müller, Siguna M. S. 3 Seah, Eric 3 Shallit, Jeffrey Outlaw 3 Teske, Edlyn 3 Thomas, Robert S. D. 3 Wooding, Kjell 2 Baillie, Robert 2 Barrucand, Pierre-A. 2 Berrizbeitia, Pedro 2 Granville, Andrew James 2 Holte, Robert C. 2 Louboutin, Stéphane R. 2 McCarthy, David 2 Patterson, Roger D. 2 Sawilla, Reginald E. 2 Schmid, B. K. 2 Silvester, Alan K. 2 te Riele, Herman 2 Wunderlich, Marvin C. 2 Zimmer, Horst Günter 1 Adleman, Leonard Max 1 Alster, Kazimierz 1 Bach, Eric 1 Ballot, Christian J. C. 1 Baniuk, L. 1 Broere, J. 1 Buell, Duncan A. 1 Buhr, P. A. 1 Cheng, K. H. F. 1 Cheng, Kell 1 Diaz y Diaz, Francisco 1 Diffie, Whitfield 1 Dubner, Harvey 1 Düllmann, Stephan 1 German, R. A. 1 Gryte, D. G. 1 Hambleton, Samuel A. 1 Hellman, Martin Edward 1 Kingsley, Roger A. 1 Kurtz, G. C. 1 Lee, Yoonjin 1 Loxton, John H. 1 Matthew, Gary K. 1 Meek, Dereck S. 1 Merkle, Ralph Charles 1 Morain, François 1 Newman, Morris 1 Pethő, Attila 1 Pohst, Michael E. 1 Purdy, George B. 1 Ramachandran, Shantha 1 Rivest, Ronald Linn 1 Sands, Jonathan W. 1 Sellers, James Allen 1 Shamir, Adi 1 Simmons, Gustavus James 1 Ströher, Harald 1 Sudler, Culbreth jun. 1 Tennenhouse, M. 1 Terras, Audrey Anne 1 Terras, Riho 1 Thiel, Christoph 1 Urbanowicz, Jerzy 1 van Rees, G. H. John 1 Washington, Lawrence C. 1 Williams, Kenneth S. all top 5 Serials 62 Mathematics of Computation 9 Acta Arithmetica 8 The Fibonacci Quarterly 6 Canadian Mathematical Bulletin 6 Pacific Journal of Mathematics 6 Proceedings of the Japan Academy. Series A 6 Utilitas Mathematica 5 Experimental Mathematics 4 Designs, Codes and Cryptography 4 Journal of Integer Sequences 4 Integers 3 Canadian Journal of Mathematics 3 Journal of Cryptology 2 The Mathematical Intelligencer 2 Ars Combinatoria 2 Journal of Number Theory 2 Journal für die Reine und Angewandte Mathematik 2 International Journal of Number Theory 2 CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC 1 Computers & Mathematics with Applications 1 Discrete Mathematics 1 IEEE Transactions on Information Theory 1 Rocky Mountain Journal of Mathematics 1 Annales des Sciences Mathématiques du Québec 1 Colloquium Mathematicum 1 Functiones et Approximatio. Commentarii Mathematici 1 Kiberneticheskiĭ Sbornik. Novaya Seriya 1 The Mathematics Student 1 Nagoya Mathematical Journal 1 Proceedings of the American Mathematical Society 1 Publicationes Mathematicae Debrecen 1 Cryptologia 1 Comptes Rendus Mathématiques de l’Académie des Sciences 1 Journal of Symbolic Computation 1 Journal of Complexity 1 Séminaire de Théorie des Nombres de Bordeaux. Deuxième Série 1 The Journal of Supercomputing 1 Elemente der Mathematik 1 Notices of the American Mathematical Society 1 Nieuw Archief voor Wiskunde. Vierde Serie 1 Journal de Théorie des Nombres de Bordeaux 1 Fundamenta Informaticae 1 Journal of the Australian Mathematical Society 1 BIT. Nordisk Tidskrift for Informationsbehandling 1 International Journal of Mathematics and Computer Science 1 Contributions to Discrete Mathematics 1 Lecture Notes in Computer Science 1 Canadian Mathematical Society Series of Monographs and Advanced Texts 1 CMS/CAIMS Books in Mathematics all top 5 Fields 208 Number theory (11-XX) 20 Information and communication theory, circuits (94-XX) 19 Field theory and polynomials (12-XX) 14 General and overarching topics; collections (00-XX) 13 Computer science (68-XX) 11 Numerical analysis (65-XX) 8 History and biography (01-XX) 4 Combinatorics (05-XX) 4 Algebraic geometry (14-XX) 1 Group theory and generalizations (20-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 175 Publications have been cited 890 times in 530 Documents Cited by ▼ Year ▼ A modification of the RSA public-key encryption procedure. Zbl 0466.94018 Williams, H. C. 30 1980 Computer verification of the Ankeny-Artin-Chowla Conjecture for all primes less than \(100 000 000 000\). Zbl 0987.11065 van der Poorten, A. J.; te Riele, H. J. J.; Williams, H. C. 26 2001 Solving the Pell equation. Zbl 1177.11027 Jacobson, Michael J. jun.; Williams, Hugh C. 26 2009 A \(p+1\) method of factoring. Zbl 0492.10004 Williams, H. C. 25 1982 A key-exchange system based on imaginary quadratic fields. Zbl 0659.94004 Buchmann, Johannes; Williams, H. C. 24 1988 Édouard Lucas and primality testing. Zbl 1155.11363 Williams, Hugh C. 24 1998 On the parallel generation of the residues for the continued fraction factoring algorithm. Zbl 0617.10005 Williams, H. C.; Wunderlich, M. C. 23 1987 On numbers analogous to the Carmichael numbers. Zbl 0368.10011 Williams, H. C. 17 1977 Numerical results on class groups of imaginary quadratic fields. Zbl 1143.11370 Jacobson, Michael J.; Ramachandran, Shantha; Williams, Hugh C. 15 2006 Key-exchange in real quadratic congruence function fields. Zbl 0851.94021 Scheidler, R.; Stein, A.; Williams, Hugh C. 15 1996 Some computer results on units in quadratic and cubic fields. Zbl 0348.12003 Beach, B. D.; Williams, H. C.; Zarnke, C. R. 14 1971 On prime valued polynomials and class numbers of real quadratic fields. Zbl 0629.12004 Mollin, R. A.; Williams, H. C. 13 1988 Short representation of quadratic integers. Zbl 0833.11060 Buchmann, Johannes; Thiel, Christoph; Williams, Hugh 13 1995 A conjecture of S. Chowla via the generalized Riemann hypothesis. Zbl 0649.12005 Mollin, R. A.; Williams, H. C. 12 1988 A computational technique for evaluating \(L(1,\chi)\) and the class number of a real quadratic field. Zbl 0345.12004 Williams, H. C.; Broere, J. 12 1976 Solution of the class number one problem for real quadratic fields of extended Richaud-Degert type (with one possible exception). Zbl 0696.12004 Mollin, R. A.; Williams, H. C. 12 1990 Primality testing on a computer. Zbl 0406.10008 Williams, H. C. 12 1978 Some algorithms for prime testing using generalized Lehmer functions. Zbl 0342.10007 Williams, H. C.; Judd, J. S. 11 1976 A computational technique for determining the class number of a pure cubic field. Zbl 0324.12005 Barrucand, Pierre; Williams, H. C.; Baniuk, L. 11 1976 Continued fractions and number-theoretic computations. Zbl 0594.12003 Williams, Hugh C. 11 1985 Computation of the class number of a real quadratic field. Zbl 0757.11036 Mollin, R. A.; Williams, H. C. 11 1992 Class numbers of real quadratic fields, continued fractions, reduced ideals, prime-producing quadratic polynomials and quadratic residue covers. Zbl 0771.11039 Louboutin, S.; Mollin, R. A.; Williams, H. C. 11 1992 Torsion groups of elliptic curves with integral j-invariant over pure cubic fields. Zbl 0734.14014 Fung, G. W.; Ströher, H.; Williams, H. C.; Zimmer, H. G. 10 1990 A key-exchange protocol using real quadratic fields. Zbl 0816.94018 Scheidler, Renate; Buchmann, Johannes A.; Williams, Hugh C. 10 1994 Some computational results on a problem concerning powerful numbers. Zbl 0642.12001 Stephens, A. J.; Williams, H. C. 9 1988 A note on the Fibonacci quotient \(F_{p-\varepsilon}/p\). Zbl 0491.10009 Williams, H. C. 9 1982 Some methods for evaluating the regulator of a real quadratic function field. Zbl 0987.11071 Stein, Andreas; Williams, Hugh C. 9 1999 Prime producing quadratic polynomials and real quadratic fields of class number one. Zbl 0695.12002 Mollin, R. A.; Williams, H. C. 9 1989 Calculation of the regulator of \(Q(\sqrt D)\) by use of the nearest integer continued fraction algorithm. Zbl 0401.10011 Williams, H. C.; Buhr, P. A. 9 1979 Some primes of the form \((a^n-1)/(a-1)\). Zbl 0417.10004 Williams, H. C.; Seah, E. 9 1979 Some results on pseudosquares. Zbl 0852.11072 Lukes, R. F.; Patterson, C. D.; Williams, H. C. 8 1996 Results and estimates on pseudopowers. Zbl 0853.11103 Bach, Eric; Lukes, Richard; Shallit, Jeffrey; Williams, H. C. 8 1996 On the imaginary bicyclic biquadratic fields with class-number 2. Zbl 0379.12002 Buell, D. A.; Williams, H. C.; Williams, K. S. 8 1977 Calculation of the regulator of a pure cubic field. Zbl 0431.12006 Williams, H. C.; Cormack, G.; Seah, E. 8 1980 An investigation of bounds for the regulator of quadratic fields. Zbl 0859.11057 Jacobson, Michael J. jun.; Lukes, Richard F.; Williams, Hugh C. 8 1995 On the infrastructure of the principal ideal class of an algebraic number field of unit rank one. Zbl 0653.12005 Buchmann, Johannes; Williams, H. C. 7 1988 New computations concerning the Cohen-Lenstra heuristics. Zbl 1050.11096 te Riele, Herman; Williams, Hugh 7 2003 Some prime numbers of the forms \(2A3^n+1\) and \(2A3^n-1\). Zbl 0259.10005 Williams, H. C.; Zarnke, C. R. 7 1972 Effective primality tests for some integers of the forms \(A5^ n-1\) and \(A7^ n-1\). Zbl 0608.10003 Williams, H. C. 7 1987 Class number one for real quadratic fields, continued fractions and reduced ideals. Zbl 0714.11067 Mollin, R. A.; Williams, H. C. 7 1989 Some remarks concerning the M.I.T. public-key cryptosystem. Zbl 0418.94010 Williams, H. C.; Schmid, B. 7 1979 The calculation of a large cubic class number with an application to real cyclotomic fields. Zbl 0527.12004 Seah, Eric; Washington, Lawrence C.; Williams, Hugh C. 6 1983 A rapid method of evaluating the regulator and class number of a pure cubic field. Zbl 0528.12004 Williams, H. C.; Dueck, G. W.; Schmid, B. K. 6 1983 A public-key cryptosystem utilizing cyclotomic fields. Zbl 0829.94005 Scheidler, Renate; Williams, Hugh C. 6 1995 Numerical sieving devices: Their history and some applications. Zbl 0856.11048 Lukes, R. F.; Patterson, C. D.; Williams, H. C. 6 1995 An upper bound for the period of the simple continued fraction for \(\sqrt D\). Zbl 0346.10005 Stanton, R. G.; Sudler, C. jun.; Williams, H. C. 6 1976 The efficiency and security of a real quadratic field based key exchange protocol. Zbl 0986.94024 Jacobson, Michael J. jun.; Scheidler, Renate; Williams, Hugh C. 6 2001 The primality of \(N = 2A3^n-1\). Zbl 0251.10009 Williams, H. C. 6 1972 Determination of the primality of \(N\) by using factors of \(N^2\pm 1\). Zbl 0322.10007 Williams, H. C.; Judd, J. S. 6 1976 On the computation of a table of complex cubic fields with discriminant \(D>-10^ 6\). Zbl 0705.11063 Fung, Gilbert W.; Williams, H. C. 6 1990 On a determination of real quadratic fields of class number one and related continued fraction period length less than 25. Zbl 0743.11062 Mollin, R. A.; Williams, H. C. 6 1991 Computation of the first factor of the class number of cyclotomic fields. Zbl 0762.11039 Fung, Gilbert; Granville, Andrew; Williams, Hugh C. 6 1992 On principal ideal testing in algebraic number fields. Zbl 0624.12007 Buchmann, Johannes; Williams, H. C. 6 1987 Construction of all cubic function fields of a given square-free discriminant. Zbl 1390.11134 Jacobson, M. J. jun.; Lee, Y.; Scheidler, R.; Williams, H. C. 6 2015 New quadratic polynomials with high densities of prime values. Zbl 1009.11060 Jacobson, Michael J. jun.; Williams, Hugh C. 6 2003 On principal ideal testing in totally complex quartic fields and the determination of certain cyclotomic constants. Zbl 0626.12006 Buchmann, Johannes; Williams, H. C. 5 1987 Some explicit upper bounds on the class number and regulator of a cubic field with negative discriminant. Zbl 0649.12003 Barrucand, Pierre; Loxton, John; Williams, H. C. 5 1987 An upper bound on the least inert prime in a real quadratic field. Zbl 1053.11092 Granville, Andrew; Mollin, R. A.; Williams, H. C. 5 2000 Some fourth-order linear divisibility sequences. Zbl 1237.11006 Williams, H. C.; Guy, R. K. 5 2011 Computation of real quadratic fields with class number one. Zbl 0699.12006 Stephens, A. J.; Williams, H. C. 5 1988 A key exchange system based on real quadratic fields. Extended abstract. Zbl 0722.68043 Buchmann, Johannes A.; Williams, Hugh C. 5 1990 Simple groups of square order and an interesting sequence of primes. Zbl 0365.20025 Newman, Morris; Shanks, Daniel; Williams, H. C. 5 1980 Some primality tests that eluded Lucas. Zbl 1364.11161 Roettger, E. L.; Williams, H. C.; Guy, R. K. 5 2015 Solving the Pell equation. Zbl 1043.11027 Williams, H. C. 5 2002 Modular arithmetic on elements of small norm in quadratic fields. Zbl 1028.11080 Jacobson, M. J. jun.; Williams, H. C. 5 2002 Some public-key crypto-functions as intractable as factorization. Zbl 0652.94012 Williams, H. C. 4 1985 On the computation of the class number of an algebraic number field. Zbl 0677.12003 Buchmann, Johannes; Williams, H. C. 4 1989 Doubly-focused enumeration of pseudosquares and pseudocubes. Zbl 1143.11360 Wooding, Kjell; Williams, Hugh C. 4 2006 A new look at an old equation. Zbl 1206.11152 Sawilla, R. E.; Silvester, A. K.; Williams, H. C. 4 2008 A class of primality tests for trinomials which includes the Lucas-Lehmer test. Zbl 0482.10007 Williams, H. C. 4 1982 Determination of principal factors in \(Q(\sqrt{D})\) and \(Q(D^{1/3})\). Zbl 0491.12006 Williams, H. C. 4 1982 On certain continued fraction expansions of fixed period length. Zbl 0926.11005 van der Poorten, A. J.; Williams, H. C. 4 1999 An improved real-quadratic-field-based key exchange procedure. Zbl 1101.68551 Jacobson, Michael J. jun.; Scheidler, Renate; Williams, Hugh C. 4 2006 An \(M^ 3\) public-key encryption scheme. Zbl 0612.94010 Williams, H. C. 4 1986 Some results concerning certain periodic continued fractions. Zbl 1080.11008 Cheng, Kell; Williams, Hugh 4 2005 Quadratic polynomials which have a high density of prime values. Zbl 0701.11035 Fung, G. W.; Williams, H. C. 4 1990 Solution of a problem of Yokoi. Zbl 0705.11060 Mollin, R. A.; Williams, H. C. 4 1990 An open architecture number sieve. Zbl 0711.11051 Stephens, A. J.; Williams, H. C. 4 1990 On a solution of a class number two problem for a family of real quadratic fields. Zbl 0734.11058 Mollin, R. A.; Williams, H. C. 4 1991 Some formulas concerning the fundamental unit of a real quadratic field. Zbl 0745.11049 Williams, H. C. 4 1991 A complete generalization of Yokoi’s \(p\)-invariants. Zbl 0762.11035 Mollin, R. A.; Williams, H. C. 4 1992 Some observations on primality testing. Zbl 0382.10005 Williams, H. C.; Holte, R. 4 1978 Quadratic fields with 3-rank equal to 4. Zbl 0409.12009 Diaz y Diaz, Francisco; Shanks, Daniel; Williams, H. C. 4 1979 A note on class-number one in pure cubic fields. Zbl 0439.12005 Williams, H. C.; Shanks, Daniel 4 1979 A note on the primality of \(6^{2^ n}+1\) and \(10^{2^ n}+1\). Zbl 0661.10009 Williams, H. C. 3 1988 The influence of computers in the development of number theory. Zbl 0486.10001 Williams, H. C. 3 1982 Some results concerning Voronoi’s continued fraction over \(Q(D^{1/3})\). Zbl 0486.12002 Williams, H. C. 3 1981 Some computational results on a problem of Eisenstein. Zbl 0689.10024 Stephens, A. J.; Williams, H. C. 3 1989 Explicit primality criteria for \((p-1) p^n-1\). Zbl 1018.11062 Stein, Andreas; Williams, H. C. 3 2000 An improved method of computing the regulator of a real quadratic function field. Zbl 0935.11048 Stein, Andreas; Williams, Hugh C. 3 1998 A note on Shanks’s chains of primes. Zbl 1032.11065 Teske, Edlyn; Williams, Hugh C. 3 2000 A report on prime numbers of the forms \(M =(6a+1) 2^{2n-1}-1\) and \(M' =(6a-1) 2^{2n} -1\). Zbl 0157.08701 Williams, H. C.; Zarnke, C. R. 3 1968 Some algorithms for solving a cubic congruence modulo \(p\). Zbl 0294.10001 Williams, H. C.; Zarnke, C. R. 3 1974 Efficient ideal reduction in quadratic fields. Zbl 1139.11044 Jacobson, Michael J. jun.; Sawilla, Reginald E.; Williams, Hugh C. 3 2006 Certain pure cubic fields with class-number one. Zbl 0356.12004 Williams, H. C. 3 1977 Computation of the class number and class group of a complex cubic field. Zbl 0576.12006 Dueck, G.; Williams, H. C. 3 1985 A note on class-number one in certain real quadratic and pure cubic fields. Zbl 0589.12003 Tennenhouse, M.; Williams, H. C. 3 1986 Graphing L-functions of Kronecker symbols in the real part of the critical strip. Zbl 0592.10038 Purdy, G.; Terras, R.; Terras, A.; Williams, H. C. 3 1985 The primality of R1031. Zbl 0602.10001 Williams, H. C.; Dubner, Harvey 3 1986 Some results concerning the nearest integer continued fraction expansion of \(\sqrt D\). Zbl 0425.10037 Williams, H. C. 3 1980 Lucas-Lehmer primality tests for certain prime curios. Zbl 1493.11156 Roettger, E. L.; Williams, H. C. 1 2021 Cubic fields with geometry. Zbl 1451.11001 Hambleton, Samuel A.; Williams, Hugh C. 2 2018 Construction of all cubic function fields of a given square-free discriminant. Zbl 1390.11134 Jacobson, M. J. jun.; Lee, Y.; Scheidler, R.; Williams, H. C. 6 2015 Some primality tests that eluded Lucas. Zbl 1364.11161 Roettger, E. L.; Williams, H. C.; Guy, R. K. 5 2015 Odd and even linear divisibility sequences of order 4. Zbl 1336.11017 Williams, H. C.; Guy, R. K. 2 2015 Some arithmetic properties of certain sequences. Zbl 1378.11022 Roettger, E. L.; Williams, H. C. 1 2015 Some extensions of the Lucas functions. Zbl 1332.11023 Roettger, E. L.; Williams, H. C.; Guy, R. K. 1 2013 Shorter compact representations in real quadratic fields. Zbl 1320.11098 Silvester, Alan K.; Jacobson, Michael J. jun.; Williams, Hugh C. 1 2013 Some monoapparitic fourth order linear divisibility sequences. Zbl 1278.11014 Williams, Hugh C.; Guy, Richard K. 2 2012 Public-key cryptography based on a cubic extension of the Lucas functions. Zbl 1237.94092 Roettger, Eric; Williams, Hugh C. 1 2012 Classification and symmetries of a family of continued fractions with bounded period length. Zbl 1322.11010 Cheng, K. H. F.; Guy, R. K.; Scheidler, R.; Williams, H. C. 1 2012 Some fourth-order linear divisibility sequences. Zbl 1237.11006 Williams, H. C.; Guy, R. K. 5 2011 Improved primality proving with Eisenstein pseudocubes. Zbl 1260.11079 Wooding, Kjell; Williams, H. C. 1 2010 Solving the Pell equation. Zbl 1177.11027 Jacobson, Michael J. jun.; Williams, Hugh C. 26 2009 A cubic extension of the Lucas functions. Zbl 1215.11010 Müller, Siguna; Roettger, Eric; Williams, Hugh C. 2 2009 A new look at an old equation. Zbl 1206.11152 Sawilla, R. E.; Silvester, A. K.; Williams, H. C. 4 2008 Sequences of Jacobian varieties with torsion divisors of quadratic order. Zbl 1188.11034 Patterson, Roger D.; van der Poorten, Alfred J.; Williams, Hugh C. 2 2008 Characterization of a generalized Shanks sequence. Zbl 1221.11211 Patterson, Roger D.; van der Poorten, Alfred J.; Williams, Hugh C. 2 2007 A fast, rigorous technique for computing the regulator of a real quadratic field. Zbl 1126.11072 de Haan, R.; Jacobson, M. J. jun.; Williams, H. C. 1 2007 Numerical results on class groups of imaginary quadratic fields. Zbl 1143.11370 Jacobson, Michael J.; Ramachandran, Shantha; Williams, Hugh C. 15 2006 Doubly-focused enumeration of pseudosquares and pseudocubes. Zbl 1143.11360 Wooding, Kjell; Williams, Hugh C. 4 2006 An improved real-quadratic-field-based key exchange procedure. Zbl 1101.68551 Jacobson, Michael J. jun.; Scheidler, Renate; Williams, Hugh C. 4 2006 Efficient ideal reduction in quadratic fields. Zbl 1139.11044 Jacobson, Michael J. jun.; Sawilla, Reginald E.; Williams, Hugh C. 3 2006 Some results concerning certain periodic continued fractions. Zbl 1080.11008 Cheng, Kell; Williams, Hugh 4 2005 Pseudocubes and primality testing. Zbl 1148.11316 Berrizbeitia, P.; Müller, S.; Williams, H. C. 2 2004 Imaginary cyclic quartic fields with large minus class numbers. Zbl 1125.11350 Jacobson, M. J. jun.; Williams, H. C.; Wooding, K. 1 2004 New computations concerning the Cohen-Lenstra heuristics. Zbl 1050.11096 te Riele, Herman; Williams, Hugh 7 2003 New quadratic polynomials with high densities of prime values. Zbl 1009.11060 Jacobson, Michael J. jun.; Williams, Hugh C. 6 2003 Solving the Pell equation. Zbl 1043.11027 Williams, H. C. 5 2002 Modular arithmetic on elements of small norm in quadratic fields. Zbl 1028.11080 Jacobson, M. J. jun.; Williams, H. C. 5 2002 Computer verification of the Ankeny-Artin-Chowla Conjecture for all primes less than \(100 000 000 000\). Zbl 0987.11065 van der Poorten, A. J.; te Riele, H. J. J.; Williams, H. C. 26 2001 The efficiency and security of a real quadratic field based key exchange protocol. Zbl 0986.94024 Jacobson, Michael J. jun.; Scheidler, Renate; Williams, Hugh C. 6 2001 Public-key cryptography and computational number theory. Proceedings of the international conference organized by the Stefan Banach International Mathematical Center, Warsaw, Poland, September 11–15, 2000. Zbl 0976.00054 1 2001 An upper bound on the least inert prime in a real quadratic field. Zbl 1053.11092 Granville, Andrew; Mollin, R. A.; Williams, H. C. 5 2000 Explicit primality criteria for \((p-1) p^n-1\). Zbl 1018.11062 Stein, Andreas; Williams, H. C. 3 2000 A note on Shanks’s chains of primes. Zbl 1032.11065 Teske, Edlyn; Williams, Hugh C. 3 2000 The size of the fundamental solutions of consecutive Pell equations. Zbl 0961.11007 Jacobson, Michael J. jun.; Williams, Hugh C. 1 2000 Some methods for evaluating the regulator of a real quadratic function field. Zbl 0987.11071 Stein, Andreas; Williams, Hugh C. 9 1999 On certain continued fraction expansions of fixed period length. Zbl 0926.11005 van der Poorten, A. J.; Williams, H. C. 4 1999 A problem concerning a character sum. Zbl 0938.11061 Teske, Edlyn; Williams, Hugh C. 2 1999 Édouard Lucas and primality testing. Zbl 1155.11363 Williams, Hugh C. 24 1998 An improved method of computing the regulator of a real quadratic function field. Zbl 0935.11048 Stein, Andreas; Williams, Hugh C. 3 1998 Daniel Shanks (1917-1996). Zbl 0908.01035 Williams, H. C. 1 1997 Daniel Shanks (1917-1996). Zbl 0867.01016 Williams, H. C. 1 1997 Key-exchange in real quadratic congruence function fields. Zbl 0851.94021 Scheidler, R.; Stein, A.; Williams, Hugh C. 15 1996 Some results on pseudosquares. Zbl 0852.11072 Lukes, R. F.; Patterson, C. D.; Williams, H. C. 8 1996 Results and estimates on pseudopowers. Zbl 0853.11103 Bach, Eric; Lukes, Richard; Shallit, Jeffrey; Williams, H. C. 8 1996 Short representation of quadratic integers. Zbl 0833.11060 Buchmann, Johannes; Thiel, Christoph; Williams, Hugh 13 1995 An investigation of bounds for the regulator of quadratic fields. Zbl 0859.11057 Jacobson, Michael J. jun.; Lukes, Richard F.; Williams, Hugh C. 8 1995 A public-key cryptosystem utilizing cyclotomic fields. Zbl 0829.94005 Scheidler, Renate; Williams, Hugh C. 6 1995 Numerical sieving devices: Their history and some applications. Zbl 0856.11048 Lukes, R. F.; Patterson, C. D.; Williams, H. C. 6 1995 A key-exchange protocol using real quadratic fields. Zbl 0816.94018 Scheidler, Renate; Buchmann, Johannes A.; Williams, Hugh C. 10 1994 Factoring integers before computers. Zbl 0847.11002 Williams, H. C.; Shallit, J. O. 2 1994 Halfway to a solution of \(x^ 2 - Dy^ 2 = -3\). Zbl 0820.11015 Mollin, R. A.; van der Poorten, A. J.; Williams, H. C. 2 1994 Quadratic residue covers for certain real quadratic fields. Zbl 0805.11080 Mollin, R. A.; Williams, H. C. 1 1994 Errata: On the computation of a table of complex cubic fields with discriminant \(D> -10^ 6\). Zbl 0835.11041 Fung, G. W.; Williams, H. C. 1 1994 How was \(F_ 6\) factored? Zbl 0779.11002 Williams, H. C. 3 1993 Class groups of exponent two in real quadratic fields. Zbl 0795.11057 Louboutin, S.; Mollin, R. A.; Williams, H. C. 1 1993 Classification and enumeration of real quadratic fields having exactly one non-inert prime less than a Minkowski bound. Zbl 0803.11054 Mollin, R. A.; Williams, H. C. 1 1993 Computation of the class number of a real quadratic field. Zbl 0757.11036 Mollin, R. A.; Williams, H. C. 11 1992 Class numbers of real quadratic fields, continued fractions, reduced ideals, prime-producing quadratic polynomials and quadratic residue covers. Zbl 0771.11039 Louboutin, S.; Mollin, R. A.; Williams, H. C. 11 1992 Computation of the first factor of the class number of cyclotomic fields. Zbl 0762.11039 Fung, Gilbert; Granville, Andrew; Williams, Hugh C. 6 1992 A complete generalization of Yokoi’s \(p\)-invariants. Zbl 0762.11035 Mollin, R. A.; Williams, H. C. 4 1992 A method of tabulating the number-theoretic function \(g(k)\). Zbl 0761.11037 Scheidler, Renate; Williams, Hugh C. 2 1992 On real quadratic fields of class number two. Zbl 0774.11061 Mollin, R. A.; Williams, H. C. 2 1992 Consecutive powers in continued fractions. Zbl 0764.11010 Mollin, R. A.; Williams, H. C. 1 1992 On a determination of real quadratic fields of class number one and related continued fraction period length less than 25. Zbl 0743.11062 Mollin, R. A.; Williams, H. C. 6 1991 On a solution of a class number two problem for a family of real quadratic fields. Zbl 0734.11058 Mollin, R. A.; Williams, H. C. 4 1991 Some formulas concerning the fundamental unit of a real quadratic field. Zbl 0745.11049 Williams, H. C. 4 1991 Affirmative solution of a conjecture related to a sequence of Shanks. Zbl 0743.11063 Mollin, R. A.; Williams, H. C. 2 1991 Implementation of a key exchange protocol using real quadratic fields. Zbl 0797.68053 Scheidler, Renate; Buchmann, Johannes A.; Williams, Hugh C. 2 1991 Some remarks concerning the complexity of computing class groups of quadratic fields. Zbl 0744.11067 Buchmann, Johannes A.; Williams, Hugh C. 1 1991 On the divisor function and class numbers of real quadratic fields. III. Zbl 0748.11053 Mollin, R. A.; Williams, H. C. 1 1991 Computational number theory. Proceedings of the colloquium on computational number theory held at the Kossuth Lajos University, Debrecen (Hungary), September 4-9, 1989. Zbl 0722.00004 1 1991 Powers of 2, continued fractions, and the class number one problem for real quadratic fields \(\mathbb{Q}(\sqrt d)\), with \(d\equiv 1\pmod 8\). Zbl 0771.11006 Mollin, R. A.; Williams, H. C. 1 1991 Solution of the class number one problem for real quadratic fields of extended Richaud-Degert type (with one possible exception). Zbl 0696.12004 Mollin, R. A.; Williams, H. C. 12 1990 Torsion groups of elliptic curves with integral j-invariant over pure cubic fields. Zbl 0734.14014 Fung, G. W.; Ströher, H.; Williams, H. C.; Zimmer, H. G. 10 1990 On the computation of a table of complex cubic fields with discriminant \(D>-10^ 6\). Zbl 0705.11063 Fung, Gilbert W.; Williams, H. C. 6 1990 A key exchange system based on real quadratic fields. Extended abstract. Zbl 0722.68043 Buchmann, Johannes A.; Williams, Hugh C. 5 1990 Quadratic polynomials which have a high density of prime values. Zbl 0701.11035 Fung, G. W.; Williams, H. C. 4 1990 Solution of a problem of Yokoi. Zbl 0705.11060 Mollin, R. A.; Williams, H. C. 4 1990 An open architecture number sieve. Zbl 0711.11051 Stephens, A. J.; Williams, H. C. 4 1990 Class number problems for real quadratic fields. Zbl 0705.11057 Mollin, R. A.; Williams, H. C. 2 1990 Quadratic fields and cryptography. Zbl 0711.11038 Buchmann, Johannes; Williams, H. C. 2 1990 On the complexity and efficiency of a new key exchange system. Zbl 0734.68047 Buchmann, Johannes A.; Düllmann, Stephan; Williams, Hugh C. 2 1990 Continued fractions of period five and real quadratic fields of class number one. Zbl 0705.11059 Mollin, R. A.; Williams, H. C. 1 1990 The period length of Voronoi’s algorithm for certain cubic orders. Zbl 0732.11055 Williams, H. C. 1 1990 Prime producing quadratic polynomials and real quadratic fields of class number one. Zbl 0695.12002 Mollin, R. A.; Williams, H. C. 9 1989 Class number one for real quadratic fields, continued fractions and reduced ideals. Zbl 0714.11067 Mollin, R. A.; Williams, H. C. 7 1989 On the computation of the class number of an algebraic number field. Zbl 0677.12003 Buchmann, Johannes; Williams, H. C. 4 1989 Some computational results on a problem of Eisenstein. Zbl 0689.10024 Stephens, A. J.; Williams, H. C. 3 1989 Quadratic non-residues and prime-producing polynomials. Zbl 0714.11066 Mollin, R. A.; Williams, H. C. 2 1989 On the existence of a short proof for the value of the class number and regulator of a real quadratic field. Zbl 0701.11048 Buchmann, Johannes; Williams, H. C. 1 1989 Period four and real quadratic fields of class number one. Zbl 0705.11058 Mollin, R. A.; Williams, H. C. 1 1989 A key-exchange system based on imaginary quadratic fields. Zbl 0659.94004 Buchmann, Johannes; Williams, H. C. 24 1988 On prime valued polynomials and class numbers of real quadratic fields. Zbl 0629.12004 Mollin, R. A.; Williams, H. C. 13 1988 A conjecture of S. Chowla via the generalized Riemann hypothesis. Zbl 0649.12005 Mollin, R. A.; Williams, H. C. 12 1988 Some computational results on a problem concerning powerful numbers. Zbl 0642.12001 Stephens, A. J.; Williams, H. C. 9 1988 On the infrastructure of the principal ideal class of an algebraic number field of unit rank one. Zbl 0653.12005 Buchmann, Johannes; Williams, H. C. 7 1988 Computation of real quadratic fields with class number one. Zbl 0699.12006 Stephens, A. J.; Williams, H. C. 5 1988 ...and 75 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 605 Authors 53 Williams, Hugh Cowie 23 Mollin, Richard Anthony 20 Scheidler, Renate 15 Jacobson, Michael John jun. 15 Louboutin, Stéphane R. 10 Buchmann, Johannes A. 10 Stein, Andreas 7 Roettger, Eric L. 6 Shallit, Jeffrey Outlaw 6 Washington, Lawrence C. 5 Azizi, Abdelmalek 5 Berrizbeitia, Pedro 5 Castagnos, Guilhem 5 Ismaili, Moulay Chrif 5 Mayer, Daniel C. 5 Morain, François 4 Aouissi, Siham 4 Biasse, Jean-François 4 Byeon, Dongho 4 Clark, Peter Louis 4 González-Jiménez, Enrique 4 Grau, José María 4 Laguillaumie, Fabien 4 Lee, Yoonjin 4 Luca, Florian 4 Lukes, Richard F. 4 Mishra, Mohit 4 Moree, Pieter 4 Murru, Nadir 4 Oller-Marcén, Antonio M. 4 Pollack, Paul 4 Pomerance, Carl Bernard 4 Sun, Zhi-Wei 4 3 Akbary, Amir 3 Bach, Eric 3 Brent, Richard Peirce 3 Cao, Zhenfu 3 Chakraborty, Kalyan 3 Cohen, Henri 3 Elia, Michele 3 Felix, Adam Tyler 3 Fung, Gilbert W. 3 Granville, Andrew James 3 Gužvić, Tomislav 3 Hoque, Azizul 3 Ichimura, Humio 3 Joye, Marc 3 Klaška, Jiří 3 Koblitz, Neal I. 3 Lee, Jungyun 3 Matthews, Keith R. 3 Nawata, Norio 3 Panario, Daniel 3 Pethő, Attila 3 Pohst, Michael E. 3 Robertson, John P. 3 Sadornil, Daniel 3 Srinivasan, Anitha 3 Tauraso, Roberto 3 Tekcan, Ahmet 3 Teske, Edlyn 3 Tomita, Koshi 3 Tran, Ha Thanh Nguyen 3 Wagstaff, Samuel Standfield jun. 2 Adam, David 2 Alexandru, Victor 2 Atkin, Arthur Oliver Lonsdale 2 Baillie, Robert 2 Bauer, Mark L. 2 Bellini, Emanuele 2 Bennett, Michael A. 2 Bernstein, Daniel Julius 2 Bhargava, Manjul 2 Booker, Andrew R. 2 Cahen, Paul-Jean 2 Chen, Yonggao 2 Cobeli, Cristian 2 Crandall, Richard E. 2 Dahl, Alexander 2 De Feo, Luca 2 Deng, Lih-Yuan 2 Dilcher, Karl 2 Dong, Xiaolei 2 Dubner, Harvey 2 Fontein, Felix 2 Fujita, Yasutsugu 2 Galbraith, Steven D. 2 Guy, Richard Kenneth 2 Hambleton, Samuel A. 2 Hendy, Michael D. 2 Hoffmann, Charlotte 2 Hofheinz, Dennis 2 Hubáček, Pavel 2 İşcan, Hülya 2 Işikay, Sevcan 2 Iskra, Boris 2 Jeans, N. S. 2 Jiang, Zhengtao 2 Kamath, Chethan ...and 505 more Authors all top 5 Cited in 136 Serials 100 Mathematics of Computation 50 Journal of Number Theory 21 Proceedings of the Japan Academy. 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Second Series 1 Acta Applicandae Mathematicae 1 Discrete & Computational Geometry 1 Facta Universitatis. Series Mathematics and Informatics 1 Applied Mathematics Letters 1 Mathematical and Computer Modelling 1 Journal of the Ramanujan Mathematical Society 1 Science in China. Series A 1 International Journal of Electronics 1 Numerical Algorithms 1 Annals of Physics 1 Glasnik Matematički. Serija III 1 Bulletin of the American Mathematical Society. New Series 1 Expositiones Mathematicae 1 Chinese Science Bulletin ...and 36 more Serials all top 5 Cited in 28 Fields 464 Number theory (11-XX) 86 Information and communication theory, circuits (94-XX) 41 Algebraic geometry (14-XX) 33 Computer science (68-XX) 15 Field theory and polynomials (12-XX) 13 Combinatorics (05-XX) 12 Group theory and generalizations (20-XX) 11 Commutative algebra (13-XX) 9 Numerical analysis (65-XX) 5 Quantum theory (81-XX) 4 History and biography (01-XX) 3 Associative rings and algebras (16-XX) 3 Special functions (33-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Functional analysis (46-XX) 2 Convex and discrete geometry (52-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Differential geometry (53-XX) 1 Manifolds and cell complexes (57-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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