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Williams, Hugh Cowie

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Author ID: williams.hugh-cowie Recent zbMATH articles by "Williams, Hugh Cowie"
Published as: Williams, H. C.; Williams, Hugh C.; Williams, Hugh
Homepage: http://people.ucalgary.ca/~hwilliam/
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all top 5

Co-Authors

58 single-authored
29 Mollin, Richard Anthony
14 Buchmann, Johannes A.
13 Jacobson, Michael John jun.
11 Zarnke, C. R.
10 Scheidler, Renate
9 Roettger, Eric L.
6 Guy, Richard Kenneth
5 Fung, Gilbert W.
5 Lukes, Richard F.
5 Shanks, Daniel C.
5 Stanton, Ralph Gordon
5 van der Poorten, Alfred J.
4 Beach, B. D.
4 Cormack, Gordon V.
4 Dueck, Gerhard W.
4 Patterson, C. D.
4 Stein, Andreas
4 Stephens, Alisa J.
3 Hartnell, Bert L.
3 Judd, J. S.
3 Müller, Siguna
3 Seah, Eric
3 Shallit, Jeffrey O.
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 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
3 Canadian Journal of Mathematics
3 Journal of Cryptology
3 Journal of Integer Sequences
3 Integers
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

Publications by Year

Citations contained in zbMATH Open

163 Publications have been cited 741 times in 459 Documents Cited by Year
A modification of the RSA public-key encryption procedure. Zbl 0466.94018
Williams, H. C.
29
1980
On the parallel generation of the residues for the continued fraction factoring algorithm. Zbl 0617.10005
Williams, H. C.; Wunderlich, M. C.
21
1987
A \(p+1\) method of factoring. Zbl 0492.10004
Williams, H. C.
20
1982
Solving the Pell equation. Zbl 1177.11027
Jacobson, Michael J. jun.; Williams, Hugh C.
20
2009
Édouard Lucas and primality testing. Zbl 1155.11363
Williams, Hugh C.
16
1998
A key-exchange system based on imaginary quadratic fields. Zbl 0659.94004
Buchmann, Johannes; Williams, H. C.
15
1988
On numbers analogous to the Carmichael numbers. Zbl 0368.10011
Williams, H. C.
15
1977
Key-exchange in real quadratic congruence function fields. Zbl 0851.94021
Scheidler, R.; Stein, A.; Williams, Hugh C.
14
1996
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.
14
2001
On prime valued polynomials and class numbers of real quadratic fields. Zbl 0629.12004
Mollin, R. A.; Williams, H. C.
11
1988
A conjecture of S. Chowla via the generalized Riemann hypothesis. Zbl 0649.12005
Mollin, R. A.; Williams, H. C.
11
1988
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
Some algorithms for prime testing using generalized Lehmer functions. Zbl 0342.10007
Williams, H. C.; Judd, J. S.
11
1976
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.
11
1976
Primality testing on a computer. Zbl 0406.10008
Williams, H. C.
11
1978
Numerical results on class groups of imaginary quadratic fields. Zbl 1143.11370
Jacobson, Michael J.; Ramachandran, Shantha; Williams, Hugh C.
11
2006
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.
10
1992
Continued fractions and number-theoretic computations. Zbl 0594.12003
Williams, Hugh C.
10
1985
A key-exchange protocol using real quadratic fields. Zbl 0816.94018
Scheidler, Renate; Buchmann, Johannes A.; Williams, Hugh C.
9
1994
Computation of the class number of a real quadratic field. Zbl 0757.11036
Mollin, R. A.; Williams, H. C.
9
1992
Some computer results on units in quadratic and cubic fields. Zbl 0348.12003
Beach, B. D.; Williams, H. C.; Zarnke, C. R.
9
1971
Some methods for evaluating the regulator of a real quadratic function field. Zbl 0987.11071
Stein, Andreas; Williams, Hugh C.
9
1999
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
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 note on the Fibonacci quotient \(F_{p-\varepsilon}/p\). Zbl 0491.10009
Williams, H. C.
8
1982
Some primes of the form \((a^n-1)/(a-1)\). Zbl 0417.10004
Williams, H. C.; Seah, E.
8
1979
Calculation of the regulator of a pure cubic field. Zbl 0431.12006
Williams, H. C.; Cormack, G.; Seah, E.
8
1980
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.
8
1990
Prime producing quadratic polynomials and real quadratic fields of class number one. Zbl 0695.12002
Mollin, R. A.; Williams, H. C.
8
1989
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.
8
1990
Some computational results on a problem concerning powerful numbers. Zbl 0642.12001
Stephens, A. J.; Williams, H. C.
7
1988
Results and estimates on pseudopowers. Zbl 0853.11103
Bach, Eric; Lukes, Richard; Shallit, Jeffrey; Williams, H. C.
7
1996
Effective primality tests for some integers of the forms \(A5^ n-1\) and \(A7^ n-1\). Zbl 0608.10003
Williams, H. C.
7
1987
On the imaginary bicyclic biquadratic fields with class-number 2. Zbl 0379.12002
Buell, D. A.; Williams, H. C.; Williams, K. S.
7
1977
Some remarks concerning the M.I.T. public-key cryptosystem. Zbl 0418.94010
Williams, H. C.; Schmid, B.
7
1979
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 principal ideal testing in algebraic number fields. Zbl 0624.12007
Buchmann, Johannes; Williams, H. C.
6
1987
Computation of the first factor of the class number of cyclotomic fields. Zbl 0762.11039
Fung, Gilbert; Granville, Andrew; Williams, Hugh C.
6
1992
Some results on pseudosquares. Zbl 0852.11072
Lukes, R. F.; Patterson, C. D.; Williams, H. C.
6
1996
Numerical sieving devices: Their history and some applications. Zbl 0856.11048
Lukes, R. F.; Patterson, C. D.; Williams, H. C.
6
1995
New quadratic polynomials with high densities of prime values. Zbl 1009.11060
Jacobson, Michael J. jun.; Williams, Hugh C.
6
2003
Some prime numbers of the forms \(2A3^n+1\) and \(2A3^n-1\). Zbl 0259.10005
Williams, H. C.; Zarnke, C. R.
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
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
Short representation of quadratic integers. Zbl 0833.11060
Buchmann, Johannes; Thiel, Christoph; Williams, Hugh
6
1995
New computations concerning the Cohen-Lenstra heuristics. Zbl 1050.11096
te Riele, Herman; Williams, Hugh
6
2003
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
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 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
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.
5
1988
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.
5
2015
The primality of \(N = 2A3^n-1\). Zbl 0251.10009
Williams, H. C.
5
1972
Simple groups of square order and an interesting sequence of primes. Zbl 0365.20025
Newman, Morris; Shanks, Daniel; Williams, H. C.
5
1980
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
Class number one for real quadratic fields, continued fractions and reduced ideals. Zbl 0714.11067
Mollin, R. A.; Williams, H. C.
5
1989
Computation of real quadratic fields with class number one. Zbl 0699.12006
Stephens, A. J.; Williams, H. C.
5
1988
Solving the Pell equation. Zbl 1043.11027
Williams, H. C.
5
2002
Some formulas concerning the fundamental unit of a real quadratic field. Zbl 0745.11049
Williams, H. C.
4
1991
Some primality tests that eluded Lucas. Zbl 1364.11161
Roettger, E. L.; Williams, H. C.; Guy, R. K.
4
2015
On the computation of the class number of an algebraic number field. Zbl 0677.12003
Buchmann, Johannes; Williams, H. C.
4
1989
Some observations on primality testing. Zbl 0382.10005
Williams, H. C.; Holte, R.
4
1978
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.
4
2001
A class of primality tests for trinomials which includes the Lucas-Lehmer test. Zbl 0482.10007
Williams, H. C.
4
1982
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
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
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 improved real-quadratic-field-based key exchange procedure. Zbl 1101.68551
Jacobson, Michael J. jun.; Scheidler, Renate; Williams, Hugh C.
3
2006
Modular arithmetic on elements of small norm in quadratic fields. Zbl 1028.11080
Jacobson, M. J. jun.; Williams, H. C.
3
2002
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
An \(M^ 3\) public-key encryption scheme. Zbl 0612.94010
Williams, H. C.
3
1986
Some public-key crypto-functions as intractable as factorization. Zbl 0652.94012
Williams, H. C.
3
1985
A note on the primality of \(6^{2^ n}+1\) and \(10^{2^ n}+1\). Zbl 0661.10009
Williams, H. C.
3
1988
Computation of the class number and class group of a complex cubic field. Zbl 0576.12006
Dueck, G.; Williams, H. C.
3
1985
Some algorithms for solving a cubic congruence modulo \(p\). Zbl 0294.10001
Williams, H. C.; Zarnke, C. R.
3
1974
Certain pure cubic fields with class-number one. Zbl 0356.12004
Williams, H. C.
3
1977
A note on Shanks’s chains of primes. Zbl 1032.11065
Teske, Edlyn; Williams, Hugh 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 numerical investigation into the length of the period of the continued fraction expansion of sqrt(D). Zbl 0476.10008
Williams, H. C.
3
1981
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 results concerning the nearest integer continued fraction expansion of \(\sqrt D\). Zbl 0425.10037
Williams, H. C.
3
1980
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 computational results on a problem of Eisenstein. Zbl 0689.10024
Stephens, A. J.; Williams, H. C.
3
1989
An open architecture number sieve. Zbl 0711.11051
Stephens, A. J.; Williams, H. C.
3
1990
A method of tabulating the number-theoretic function \(g(k)\). Zbl 0761.11037
Scheidler, Renate; Williams, Hugh C.
2
1992
A complete generalization of Yokoi’s \(p\)-invariants. Zbl 0762.11035
Mollin, R. A.; Williams, H. C.
2
1992
On real quadratic fields of class number two. Zbl 0774.11061
Mollin, R. A.; Williams, H. C.
2
1992
Odd and even linear divisibility sequences of order 4. Zbl 1336.11017
Williams, H. C.; Guy, R. K.
2
2015
Fast primality tests for numbers less than 50 \(\cdot \,10^ 9\). Zbl 0594.10001
Kurtz, G. C.; Shanks, Daniel; Williams, H. C.
2
1986
Some periodic continued fractions with long periods. Zbl 0565.10008
Patterson, C. D.; Williams, H. C.
2
1985
How was \(F_ 6\) factored? Zbl 0779.11002
Williams, H. C.
2
1993
An analogue of the nearest integer continued fraction for certain cubic irrationalities. Zbl 0544.10032
Williams, H. C.; Dueck, G. W.
2
1984
Cubic fields with geometry. Zbl 1451.11001
Hambleton, Samuel A.; Williams, Hugh C.
1
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.
5
2015
Some primality tests that eluded Lucas. Zbl 1364.11161
Roettger, E. L.; Williams, H. C.; Guy, R. K.
4
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
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
Some fourth-order linear divisibility sequences. Zbl 1237.11006
Williams, H. C.; Guy, R. K.
5
2011
Solving the Pell equation. Zbl 1177.11027
Jacobson, Michael J. jun.; Williams, Hugh C.
20
2009
A cubic extension of the Lucas functions. Zbl 1215.11010
Müller, Siguna; Roettger, Eric; Williams, Hugh C.
1
2009
A new look at an old equation. Zbl 1206.11152
Sawilla, R. E.; Silvester, A. K.; Williams, H. C.
2
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.
1
2008
Characterization of a generalized Shanks sequence. Zbl 1221.11211
Patterson, Roger D.; van der Poorten, Alfred J.; Williams, Hugh C.
1
2007
Numerical results on class groups of imaginary quadratic fields. Zbl 1143.11370
Jacobson, Michael J.; Ramachandran, Shantha; Williams, Hugh C.
11
2006
An improved real-quadratic-field-based key exchange procedure. Zbl 1101.68551
Jacobson, Michael J. jun.; Scheidler, Renate; Williams, Hugh C.
3
2006
Doubly-focused enumeration of pseudosquares and pseudocubes. Zbl 1143.11360
Wooding, Kjell; Williams, Hugh C.
2
2006
Efficient ideal reduction in quadratic fields. Zbl 1139.11044
Jacobson, Michael J. jun.; Sawilla, Reginald E.; Williams, Hugh C.
1
2006
Some results concerning certain periodic continued fractions. Zbl 1080.11008
Cheng, Kell; Williams, Hugh
1
2005
Imaginary cyclic quartic fields with large minus class numbers. Zbl 1125.11350
Jacobson, M. J. jun.; Williams, H. C.; Wooding, K.
1
2004
New quadratic polynomials with high densities of prime values. Zbl 1009.11060
Jacobson, Michael J. jun.; Williams, Hugh C.
6
2003
New computations concerning the Cohen-Lenstra heuristics. Zbl 1050.11096
te Riele, Herman; Williams, Hugh
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.
3
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.
14
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.
4
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
A note on Shanks’s chains of primes. Zbl 1032.11065
Teske, Edlyn; Williams, Hugh C.
3
2000
Explicit primality criteria for \((p-1) p^n-1\). Zbl 1018.11062
Stein, Andreas; Williams, H. C.
2
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.
2
1999
A problem concerning a character sum. Zbl 0938.11061
Teske, Edlyn; Williams, Hugh C.
1
1999
Édouard Lucas and primality testing. Zbl 1155.11363
Williams, Hugh C.
16
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.
14
1996
Results and estimates on pseudopowers. Zbl 0853.11103
Bach, Eric; Lukes, Richard; Shallit, Jeffrey; Williams, H. C.
7
1996
Some results on pseudosquares. Zbl 0852.11072
Lukes, R. F.; Patterson, C. D.; Williams, H. C.
6
1996
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
Numerical sieving devices: Their history and some applications. Zbl 0856.11048
Lukes, R. F.; Patterson, C. D.; Williams, H. C.
6
1995
Short representation of quadratic integers. Zbl 0833.11060
Buchmann, Johannes; Thiel, Christoph; Williams, Hugh
6
1995
A public-key cryptosystem utilizing cyclotomic fields. Zbl 0829.94005
Scheidler, Renate; Williams, Hugh C.
6
1995
A key-exchange protocol using real quadratic fields. Zbl 0816.94018
Scheidler, Renate; Buchmann, Johannes A.; Williams, Hugh C.
9
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
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
Factoring integers before computers. Zbl 0847.11002
Williams, H. C.; Shallit, J. O.
1
1994
How was \(F_ 6\) factored? Zbl 0779.11002
Williams, H. C.
2
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
Class groups of exponent two in real quadratic fields. Zbl 0795.11057
Louboutin, S.; Mollin, R. A.; Williams, H. C.
1
1993
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.
10
1992
Computation of the class number of a real quadratic field. Zbl 0757.11036
Mollin, R. A.; Williams, H. C.
9
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 method of tabulating the number-theoretic function \(g(k)\). Zbl 0761.11037
Scheidler, Renate; Williams, Hugh C.
2
1992
A complete generalization of Yokoi’s \(p\)-invariants. Zbl 0762.11035
Mollin, R. A.; Williams, H. 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
Some formulas concerning the fundamental unit of a real quadratic field. Zbl 0745.11049
Williams, H. C.
4
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 remarks concerning the complexity of computing class groups of quadratic fields. Zbl 0744.11067
Buchmann, Johannes A.; Williams, Hugh C.
1
1991
Affirmative solution of a conjecture related to a sequence of Shanks. Zbl 0743.11063
Mollin, R. A.; Williams, H. 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
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
Implementation of a key exchange protocol using real quadratic fields. Zbl 0797.68053
Scheidler, Renate; Buchmann, Johannes A.; Williams, Hugh C.
1
1991
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.
8
1990
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.
8
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
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.
3
1990
A key exchange system based on real quadratic fields. Extended abstract. Zbl 0722.68043
Buchmann, Johannes A.; Williams, Hugh C.
2
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
The period length of Voronoi’s algorithm for certain cubic orders. Zbl 0732.11055
Williams, H. C.
1
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
Prime producing quadratic polynomials and real quadratic fields of class number one. Zbl 0695.12002
Mollin, R. A.; Williams, H. C.
8
1989
Class number one for real quadratic fields, continued fractions and reduced ideals. Zbl 0714.11067
Mollin, R. A.; Williams, H. C.
5
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.
15
1988
On prime valued polynomials and class numbers of real quadratic fields. Zbl 0629.12004
Mollin, R. A.; Williams, H. C.
11
1988
A conjecture of S. Chowla via the generalized Riemann hypothesis. Zbl 0649.12005
Mollin, R. A.; Williams, H. C.
11
1988
Some computational results on a problem concerning powerful numbers. Zbl 0642.12001
Stephens, A. J.; Williams, H. C.
7
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.
5
1988
Computation of real quadratic fields with class number one. Zbl 0699.12006
Stephens, A. J.; Williams, H. C.
5
1988
A note on the primality of \(6^{2^ n}+1\) and \(10^{2^ n}+1\). Zbl 0661.10009
Williams, H. C.
3
1988
On the parallel generation of the residues for the continued fraction factoring algorithm. Zbl 0617.10005
Williams, H. C.; Wunderlich, M. C.
21
1987
Effective primality tests for some integers of the forms \(A5^ n-1\) and \(A7^ n-1\). Zbl 0608.10003
Williams, H. C.
7
1987
On principal ideal testing in algebraic number fields. Zbl 0624.12007
Buchmann, Johannes; Williams, H. C.
6
1987
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
A note on class-number one in certain real quadratic and pure cubic fields. Zbl 0589.12003
Tennenhouse, M.; Williams, H. C.
3
1986
The primality of R1031. Zbl 0602.10001
Williams, H. C.; Dubner, Harvey
3
1986
An \(M^ 3\) public-key encryption scheme. Zbl 0612.94010
Williams, H. C.
3
1986
Fast primality tests for numbers less than 50 \(\cdot \,10^ 9\). Zbl 0594.10001
Kurtz, G. C.; Shanks, Daniel; Williams, H. C.
2
1986
...and 63 more Documents
all top 5

Cited by 520 Authors

49 Williams, Hugh Cowie
23 Mollin, Richard Anthony
18 Scheidler, Renate
14 Louboutin, Stéphane R.
13 Jacobson, Michael John jun.
10 Buchmann, Johannes A.
10 Stein, Andreas
6 Shallit, Jeffrey O.
5 Berrizbeitia, Pedro
5 Roettger, Eric L.
4 Aouissi, Siham
4 Azizi, Abdelmalek
4 Byeon, Dongho
4 González-Jiménez, Enrique
4 Grau, José María
4 Ismaili, Moulay Chrif
4 Luca, Florian
4 Lukes, Richard F.
4 Mayer, Daniel C.
4 Morain, François
4 Moree, Pieter
4 Oller-Marcén, Antonio M.
4 Pomerance, Carl Bernard
4 Sun, Zhi-Wei
4
3 Bach, Eric
3 Brent, Richard Peirce
3 Cao, Zhenfu
3 Castagnos, Guilhem
3 Chakraborty, Kalyan
3 Clark, Peter Louis
3 Elia, Michele
3 Felix, Adam Tyler
3 Fung, Gilbert W.
3 Granville, Andrew James
3 Hoque, Azizul
3 Ichimura, Humio
3 Joye, Marc
3 Koblitz, Neal I.
3 Lee, Jungyun
3 Lee, Yoonjin
3 Matthews, Keith R.
3 Mishra, Mohit
3 Murru, Nadir
3 Nawata, Norio
3 Panario, Daniel
3 Pethő, Attila
3 Pohst, Michael E.
3 Pollack, Paul
3 Robertson, John P.
3 Sadornil, Daniel
3 Srinivasan, Anitha
3 Teske, Edlyn
3 Tomita, Koshi
3 Wagstaff, Samuel Standfield jun.
3 Washington, Lawrence C.
2 Adam, David
2 Akbary, Amir
2 Atkin, Arthur Oliver Lonsdale
2 Baillie, Robert
2 Bauer, Mark L.
2 Bellini, Emanuele
2 Bernstein, Daniel Julius
2 Bhargava, Manjul
2 Biasse, Jean-François
2 Booker, Andrew R.
2 Cahen, Paul-Jean
2 Chen, Yonggao
2 Cohen, Henri
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 Fujita
2 Guy, Richard Kenneth
2 Hambleton, Samuel A.
2 Hendy, Michael D.
2 Hofheinz, Dennis
2 İşcan, Hülya
2 Iskra, Boris
2 Jeans, N. S.
2 Jiang, Zhengtao
2 Karaali, Fitnat
2 Karaatli, Olcay
2 Kawamoto, Fuminori
2 Keskin, Refik
2 Kiltz, Eike
2 Klaška, Jiří
2 Laguillaumie, Fabien
2 Lamzouri, Youness
2 Lange, Tanja
2 Lenstra, Hendrik W. jun.
2 Loxton, John H.
2 Lu, Henry Horng-Shing
2 Marques, Sophie
2 McIntosh, Richard J.
...and 420 more Authors
all top 5

Cited in 119 Serials

100 Mathematics of Computation
48 Journal of Number Theory
21 Proceedings of the Japan Academy. Series A
14 Journal of Cryptology
13 International Journal of Number Theory
10 Proceedings of the American Mathematical Society
9 Journal de Théorie des Nombres de Bordeaux
8 Rocky Mountain Journal of Mathematics
7 Designs, Codes and Cryptography
7 Experimental Mathematics
5 Computers & Mathematics with Applications
5 Nagoya Mathematical Journal
5 Journal of Symbolic Computation
5 Applicable Algebra in Engineering, Communication and Computing
4 Bulletin of the Australian Mathematical Society
4 Discrete Mathematics
4 The Mathematical Intelligencer
4 Acta Arithmetica
4 Annales de l’Institut Fourier
4 Applied Mathematics and Computation
4 Archiv der Mathematik
4 Czechoslovak Mathematical Journal
4 Journal of Soviet Mathematics
4 Theoretical Computer Science
4 The Ramanujan Journal
4 Journal of Integer Sequences
4 Integers
3 Periodica Mathematica Hungarica
3 BIT
3 Transactions of the American Mathematical Society
3 Acta Mathematica Hungarica
3 Journal of Complexity
3 Kyushu Journal of Mathematics
3 Journal of Mathematical Cryptology
2 Discrete Applied Mathematics
2 Information Processing Letters
2 Israel Journal of Mathematics
2 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
2 Duke Mathematical Journal
2 Functiones et Approximatio. Commentarii Mathematici
2 Inventiones Mathematicae
2 Journal of Algebra
2 Journal of Computational and Applied Mathematics
2 Journal of Pure and Applied Algebra
2 Mathematics and Computers in Simulation
2 Mathematische Zeitschrift
2 Mathematika
2 Pacific Journal of Mathematics
2 Results in Mathematics
2 Tokyo Journal of Mathematics
2 Advances in Applied Mathematics
2 Séminaire de Théorie des Nombres de Bordeaux. Deuxième Série
2 The Journal of Supercomputing
2 Finite Fields and their Applications
2 Wuhan University Journal of Natural Sciences (WUJNS)
2 Journal of Discrete Mathematical Sciences & Cryptography
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Advances in Mathematics of Communications
2 Acta Mathematica Universitatis Ostraviensis
2 Annales Mathématiques du Québec
2 ISRN Combinatorics
2 Research in Number Theory
1 American Mathematical Monthly
1 Archive for History of Exact Sciences
1 Indian Journal of Pure & Applied Mathematics
1 Linear and Multilinear Algebra
1 Mathematical Notes
1 Advances in Mathematics
1 Computing
1 Indiana University Mathematics Journal
1 International Journal of Mathematics and Mathematical Sciences
1 Journal of the Mathematical Society of Japan
1 The Journal of Symbolic Logic
1 Manuscripta Mathematica
1 Mathematische Annalen
1 Mathematica Slovaca
1 Monatshefte für Mathematik
1 Osaka Journal of Mathematics
1 Proceedings of the Edinburgh Mathematical Society. Series II
1 Tohoku Mathematical Journal. Second Series
1 Bulletin of the Korean Mathematical Society
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 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 Indagationes Mathematicae. New Series
1 Cybernetics and Systems Analysis
1 Russian Mathematics
1 Tatra Mountains Mathematical Publications
1 Journal of Mathematical Sciences (New York)
1 Science in China. Series E
1 Abstract and Applied Analysis
...and 19 more Serials

Citations by Year

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