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» Hugh Williams
Hugh Williams
Professor
Director
- ISPIA
Pure Mathematics
+1 (403) 220-6322
MS 360
williams@math.ucalgary.ca
http://www.math.ucalgary.ca/~hwilliam
http://ispia.ucalgary.ca
Research Interests
Algebra and Number Theory:
Computational Number Theory
General:
Hardware devices
Currently Teaching
Not currently teaching any courses.
view past courses
Publications
Book
Williams, Hugh
.
Solving the {P}ell equationÂ
A K Peters, 2002. 397-435.
Teske, Edlyn and
Williams, Hugh
.
A note on {S}hanks's chains of primes
1838. Springer, 2000. 563-580.
Stein, Andreas and
Williams, Hugh
.
An improved method of computing the regulator of a real quadratic function field
1423. Springer, 1998. 607-620.
Teske, E. and
Williams, Hugh
.
A problem concerning a character sum (extended abstract)
1423. Springer, 1998. 351-357.
Williams, Hugh
.
\'{E}douard {L}ucas and primality testing
, John Wiley \& Sons Inc., 1998. x+525.
Buchmann, Johannes , Thiel, Christoph and
Williams, Hugh
.
Short representation of quadratic integers
325. Kluwer Acad. Publ., 1995. 159-185.
Williams, Hugh
and Shallit, J. O.
.
Factoring integers before computers
48. Amer. Math. Soc., 1994. 481-531.
Louboutin, S. ,
Mollin, Richard
and
Williams, Hugh
.
Class groups of exponent two in real quadratic fields
, Oxford Univ. Press, 1993. 499-513.
Mollin, Richard
and
Williams, Hugh
.
On a solution of a class number two problem for a family of real quadratic fields
de Gruyter, 1991. 95-101.
Mollin, Richard
and
Williams, Hugh
.
Powers of {$2,$} continued fractions, and the class number one problem for real quadratic fields {${\bf Q}(\sqrt d),$} with {$d\equiv 1\pmod 8$}
World Sci. Publishing, 1991. 505-516.
Buchmann, Johannes A. and
Williams, Hugh
.
A key exchange system based on real quadratic fields (extended abstract)
435. Springer, 1990. 335-343.
Mollin, Richard
and
Williams, Hugh
.
Solution of the class number one problem for real quadratic fields of extended {R}ichaud-{D}egert type (with one possible exception)
de Gruyter, 1990. 417-425.
Buchmann, Johannes A., D{\"u}llmann, Stephan and
Williams, Hugh
.
On the complexity and efficiency of a new key exchange system
434. Springer, 1990. 597-616.
Mollin, Richard
and
Williams, Hugh
.
Class number problems for real quadratic fields
154. Cambridge Univ. Press, 1990. 177-195.
Stephens, A. J. and
Williams, Hugh
.
An open architecture number sieve
154. Cambridge Univ. Press, 1990. 38-75.
Buchmann, Johannes and
Williams, Hugh
.
Quadratic fields and cryptography
154. Cambridge Univ. Press, 1990. 9-25.
Mollin, Richard
and
Williams, Hugh
.
Class number one for real quadratic fields, continued fractions and reduced ideals
265. Kluwer Acad. Publ., 1989. 481-496.
Buchmann, Johannes and
Williams, Hugh
.
On the existence of a short proof for the value of the class number and regulator of a real quadratic field
265. Kluwer Acad. Publ., 1989. 327-345.
Stephens, A. J. and
Williams, Hugh
.
Some computational results on a problem of {E}isenstein
de Gruyter, 1989. 869-886.
Mollin, Richard
and
Williams, Hugh
.
Prime producing quadratic polynomials and real quadratic fields of class number one
de Gruyter, 1989. 654-663.
Williams, Hugh
.
An {$M\sp 3$} public-key encryption scheme
218. Springer, 1986. 358-368.
Williams, Hugh
.
Some public-key crypto-functions as intractable as factorization (extended abstract)
196. Springer, 1985. 66-70.
Williams, Hugh
.
An overview of factoring
Plenum, 1984. 71-80.
Williams, Hugh
.
Computationally ``hard'' problems as a source for cryptosystems
69. Westview, 1982. 11-39.
Stanton, R. G. and
Williams, Hugh
.
Computation of some number-theoretic coverings
884. Springer, 1981. 8-13.
Williams, Hugh
.
A generalization of the {F}ibonacci numbers
Louisiana State Univ., 1970. 340-356.
Book Chapter
Jacobson, Michael,
Scheidler, Renate
and
Williams, Hugh
.
The efficiency and security of a real quadratic field-based key exchange protocol
Berlin:
de Gruyter & Co. Publishers
, 2001. 89-112.
Conference Proceedings
Wooding, Kjell
and
Williams, Hugh
.
Doubly-focused enumeration of Pseudosquares and Pseudocubes
4076 Springer-Verlag, 2006. 208-221.
Scheidler, Renate
, Buchmann, Johannes and
Williams, Hugh
.
Implementation of a key exchange protocol using real quadratic fields (extended abstract)
1991.
Journal Paper
Jacobson, M.J.,
Scheidler, Renate
and
Williams, Hugh
.
An improved real quadratic field based key exchange procedure
19.2 2006. 211-239.
Poorten, A. J., Riele, H. J. J. and
Williams, Hugh
.
Corrigenda and addition to: ``{C}omputer verification of the {A}nkeny-{A}rtin-{C}howla conjecture for all primes less than {$100\,000\,000\,000$}'' [{M}ath.\ {C}omp.\ {\bf 70} (2001), no. 235, 1311-1328; \refmr {MR}1709160 (2001j:11125)\endrefmr]
72.241 2003. 521-523 (electronic).
Jacobson, Jr. and
Williams, Hugh
.
New quadratic polynomials with high densities of prime values
72.241 2003. 499-519 (electronic).
Riele, Herman and
Williams, Hugh
.
New computations concerning the {C}ohen-{L}enstra heuristics
12.1 2003. 99-113.
Jacobson, Jr. and
Williams, Hugh
.
Modular arithmetic on elements of small norm in quadratic fields
27.1-2 2002. 93-110.
Sellers, James A. and
Williams, Hugh
.
On the infinitude of composite {NSW} numbers
40.3 2002. 253-254.
Poorten, A. J., Riele, H. J. J. and
Williams, Hugh
.
Computer verification of the {A}nkeny-{A}rtin-{C}howla conjecture for all primes less than {$100\,000\,000\,000$}
70.235 2001. 1311-1328.
Stein, Andreas and
Williams, Hugh
.
Explicit primality criteria for {$(p-1)p\sp n-1$}
69.232 2000. 1721-1734.
Granville, Andrew ,
Mollin, Richard
and
Williams, Hugh
.
An upper bound on the least inert prime in a real quadratic field
52.2 2000. 369-380.
Jacobson, Jr. and
Williams, Hugh
.
The size of the fundamental solutions of consecutive {P}ell equations
9.4 2000. 631-640.
Williams, Hugh
.
A number theoretic function arising from continued fractions
38.3 2000. 201-211.
Poorten, A. J. and
Williams, Hugh
.
On certain continued fraction expansions of fixed period length
89.1 1999. 23-35.
Teske, Edlyn and
Williams, Hugh
.
A problem concerning a character sum
8.1 1999. 63-72.
Stein, Andreas and
Williams, Hugh
.
Some methods for evaluating the regulator of a real quadratic function field
8.2 1999. 119-133.
Williams, Hugh
.
Daniel {S}hanks (1917-1996)
66.219 1997. 929-934.
Lukes, Richard F.,
Scheidler, Renate
and
Williams, Hugh
.
Further tabulation of the Erdos-Selfridge function
66.220 1997. 1709-1717.
Lukes, R. F., Patterson, C. D. and
Williams, Hugh
.
Some results on pseudosquares
65.213 John Wiley & Sons Inc., 1996. 361-372, S25-S27.
Bach, Eric , Lukes, Richard , Shallit, Jeffrey and
Williams, Hugh
.
Results and estimates on pseudopowers
65.216 John Wiley & Sons Inc., 1996. 1737-1747.
Scheidler, Renate
, Stein, Andreas and
Williams, Hugh
.
Key-exchange in real quadratic congruence function fields
7.1-2 1996. 153-174.
Mollin, Richard
and
Williams, Hugh
.
Corrigenda for: ``{A} conjecture of {S}. {C}howla via the generalized {R}iemann hypothesis'' [{P}roc.\ {A}mer.\ {M}ath.\ {S}oc. {\bf 102} (1988), no.\ 4, 794-796; \refmr {MR}0934844 (89d:11090)\endrefmr]
123.3 1995. 975.
Mollin, Richard
and
Williams, Hugh
.
Proof, disproof and advances concerning certain conjectures on real quadratic fields {$\bold Q(\sqrt{N\sp 2+4})$}
47.5 1995. 1023-1036.
Williams, Hugh
.
Some generalizations of the {$S\sb n$} sequence of {S}hanks
69.3 John Wiley & Sons Inc., 1995. 199-215.
Lukes, R. F., Patterson, C. D. and
Williams, Hugh
.
Numerical sieving devices: their history and some applications
13.1 John Wiley & Sons Inc., 1995. 113-139.
Jacobson, Jr. , Lukes, Richard F. and
Williams, Hugh
.
An investigation of bounds for the regulator of quadratic fields
4.3 John Wiley & Sons Inc., 1995. 211-225.
Shallit, Jeffrey ,
Williams, Hugh
and Morain, Fran
.
Discovery of a lost factoring machine
17.3 John Wiley & Sons Inc., 1995. 41-47.
Scheidler, Renate
and
Williams, Hugh
.
A public-key cryptosystem utilizing cyclotomic fields
6.2 1995. 117-131.
Mollin, Richard
, Poorten, A. J. and
Williams, Hugh
.
Halfway to a solution of {$X\sp 2-DY\sp 2=-3$}
6.2 1994. 421-457.
Fung, G. W. and
Williams, Hugh
.
Errata: ``{O}n the computation of a table of complex cubic fields with discriminant {$D>-10\sp 6$}'' [{M}ath.\ {C}omp.\ {\bf 55} (1990), no.\ 191, 313-325; \refmr {MR}1023760 (90m:11155)\endrefmr]
63.207 John Wiley & Sons Inc., 1994. 433.
Mollin, Richard
and
Williams, Hugh
.
Quadratic residue covers for certain real quadratic fields
62.206 1994. 885-897.
Scheidler, Renate
, Buchmann, Johannes and
Williams, Hugh
.
A key exchange protocol using real quadratic fields
7.3 1994. 171-199.
Mollin, Richard
and
Williams, Hugh
.
Classification and enumeration of real quadratic fields having exactly one noninert prime less than a {M}inkowski bound
36.1 1993. 108-115.
Williams, Hugh
.
How was {$F\sb 6$} factored?
61.203 John Wiley & Sons Inc., 1993. 463-474.
Mollin, Richard
and
Williams, Hugh
.
Computation of the class number of a real quadratic field
41. 1992. 259-308.
Mollin, Richard
and
Williams, Hugh
.
A complete generalization of {Y}okoi's {$p$}-invariants
63.2 1992. 285-294.
Mollin, Richard
and
Williams, Hugh
.
On the period length of some special continued fractions
4.1 1992. 19-42.
Mollin, Richard
and
Williams, Hugh
.
On real quadratic fields of class number two
59.200 1992. 625-632.
Louboutin, S. ,
Mollin, Richard
and
Williams, Hugh
.
Class numbers of real quadratic fields, continued fractions, reduced ideals, prime-producing quadratic polynomials and quadratic residue covers
44.4 1992. 824-842.
Fung, Gilbert , Granville, Andrew and
Williams, Hugh
.
Computation of the first factor of the class number of cyclotomic fields
42.3 John Wiley & Sons Inc., 1992. 297-312.
Mollin, Richard
and
Williams, Hugh
.
Consecutive powers in continued fractions
61.3 1992. 233-264.
Scheidler, Renate
and
Williams, Hugh
.
A method of tabulating the number-theoretic function g(k)
59.199 1992. 251-257.
Williams, Hugh
.
Some formulas concerning the fundamental unit of a real quadratic field
92.1-3 1991. 431-440.
Mollin, Richard
and
Williams, Hugh
.
Corrigenda for: ``{S}olution of a problem of {Y}okoi'' [{P}roc.\ {J}apan {A}cad.\ {S}er.\ {A} {M}ath.\ {S}ci.\ {\bf 66} (1990), no.\ 6, 141-145; \refmr {MR}1065792 (91k:11094)\endrefmr]
67.7 1991. 253.
Mollin, Richard
and
Williams, Hugh
.
On the divisor function and class numbers of real quadratic fields. {III}
67.10 1991. 338-342.
Mollin, Richard
and
Williams, Hugh
.
Affirmative solution of a conjecture related to a sequence of {S}hanks
67.3 1991. 70-72.
Mollin, Richard
and
Williams, Hugh
.
On a determination of real quadratic fields of class number one and related continued fraction period length less than {$25$}
67.1 1991. 20-25.
Buchmann, Johannes A. and
Williams, Hugh
.
Some remarks concerning the complexity of computing class groups of quadratic fields
7.3 1991. 311-315.
Fung, Gilbert W. and
Williams, Hugh
.
On the computation of a table of complex cubic fields with discriminant {$D>-10\sp 6$}
55.191 1990. 313-325.
Fung, G. W. and
Williams, Hugh
.
Quadratic polynomials which have a high density of prime values
55.191 1990. 345-353.
Buchmann, J. , Sands, J. W. and
Williams, Hugh
.
{$p$}-adic computation of real quadratic class numbers
54.190 1990. 855-868.
Fung, G. W., Str{\"o}her, H. ,
Williams, Hugh
and Zimmer, H. G.
.
Torsion groups of elliptic curves with integral {$j$}-invariant over pure cubic fields
36.1 1990. 12-45.
Mollin, Richard
and
Williams, Hugh
.
Solution of a problem of {Y}okoi
66.6 1990. 141-145.
Williams, Hugh
.
The period length of {V}orono\u\i's algorithm for certain cubic orders
37.3-4 1990. 245-265.
Mollin, Richard
and
Williams, Hugh
.
Continued fractions of period five and real quadratic fields of class number one
56.1 1990. 55-63.
Williams, Hugh
.
Eisenstein's problem and continued fractions
37. 1990. 145-157.
Mollin, Richard
and
Williams, Hugh
.
Quadratic nonresidues and prime-producing polynomials
32.4 1989. 474-478.
Buchmann, Johannes and
Williams, Hugh
.
On the computation of the class number of an algebraic number field
53.188 1989. 679-688.
Mollin, Richard
and
Williams, Hugh
.
Period four and real quadratic fields of class number one
65.4 1989. 89-93.
Mollin, Richard
and
Williams, Hugh
.
Real quadratic fields of class number one and continued fraction period less than six
11.2 1989. 51-56.
Mollin, Richard
and
Williams, Hugh
.
A conjecture of {S}. {C}howla via the generalized {R}iemann hypothesis
102.4 1988. 794-796.
Williams, Hugh
.
Corrigenda: ``{C}omputation of the class number and class group of a complex cubic field'' [{M}ath.\ {C}omp.\ {\bf 45} (1985), no.\ 171, 223-231; \refmr {MR}0790655 (86m:11078)\endrefmr] by {G}.\ {W}.\ {D}ueck and {W}illiams
50.182 1988. 655-657.
Stephens, A. J. and
Williams, Hugh
.
Computation of real quadratic fields with class number one
51.184 1988. 809-824.
Stephens, A. J. and
Williams, Hugh
.
Some computational results on a problem concerning powerful numbers
50.182 1988. 619-632.
Buchmann, Johannes and
Williams, Hugh
.
On the infrastructure of the principal ideal class of an algebraic number field of unit rank one
50.182 1988. 569-579.
Mollin, Richard
and
Williams, Hugh
.
On prime valued polynomials and class numbers of real quadratic fields
112. 1988. 143-151.
Williams, Hugh
.
A note on the primality of {$6\sp {2\sp n}+1$} and {$10\sp {2\sp n}+1$}
26.4 1988. 296-305.
Buchmann, Johannes and
Williams, Hugh
.
A key-exchange system based on imaginary quadratic fields
1.2 1988. 107-118.
Barrucand, Pierre , Loxton, John and
Williams, Hugh
.
Some explicit upper bounds on the class number and regulator of a cubic field with negative discriminant
128.2 1987. 209-222.
Williams, Hugh
and Wunderlich, M. C.
.
On the parallel generation of the residues for the continued fraction factoring algorithm
48.177 1987. 405-423.
Williams, Hugh
.
Effective primality tests for some integers of the forms {$A5\sp n-1$} and {$A7\sp n-1$}
48.177 1987. 385-403.
Buchmann, Johannes and
Williams, Hugh
.
On principal ideal testing in totally complex quartic fields and the determination of certain cyclotomic constants
48.177 1987. 55-66.
Buchmann, Johannes and
Williams, Hugh
.
On principal ideal testing in algebraic number fields
4.1 1987. 11-19.
Williams, Hugh
.
The spacing of the minima in certain cubic lattices
124.2 1986. 483-496.
Williams, Hugh
and Dubner, Harvey
.
The primality of {$R1031$}
47.176 1986. 703-711.
Kurtz, G. C., Shanks, Daniel and
Williams, Hugh
.
Fast primality tests for numbers less than $50cdot 10sp 9$
46.174 1986. 691-701.
Tennenhouse, M. and
Williams, Hugh
.
A note on class-number one in certain real quadratic and pure cubic fields
46.173 1986. 333-336.
Dueck, G. and
Williams, Hugh
.
Computation of the class number and class group of a complex cubic field
45.171 1985. 223-231.
Patterson, C. D. and
Williams, Hugh
.
Some periodic continued fractions with long periods
44.170 1985. 523-532.
Williams, Hugh
.
Continued fractions and number-theoretic computations
15.2 1985. 621-655.
Williams, Hugh
.
Some public-key crypto-functions as intractable as factorization
9.3 1985. 223-237.
Williams, Hugh
.
A note on the period length of the continued fraction expansion of certain {$\sqrt D$}
28. 1985. 201-209.
Williams, Hugh
.
On mid-period criteria for the nearest integer continued fraction expansion of {$\sqrt D$}
27. 1985. 169-185.
Williams, Hugh
and Dueck, G. W.
.
An analogue of the nearest integer continued fraction for certain cubic irrationalities
42.166 1984. 683-705.
Williams, Hugh
.
Factoring on a computer
6.3 1984. 29-36.
Seah, Eric , Washington, Lawrence C. and
Williams, Hugh
.
The calculation of a large cubic class number with an application to real cyclotomic fields
41.163 1983. 303-305.
Williams, Hugh
, Dueck, G. W. and Schmid, B. K.
.
A rapid method of evaluating the regulator and class number of a pure cubic field
41.163 1983. 235-286.
Patterson, C. D. and
Williams, Hugh
.
A report on the {U}niversity of {M}anitoba {S}ieve {U}nit
37. 1983. 85-98.
Williams, Hugh
.
A note on the {F}ibonacci quotient {$F\sb{p-\varepsilon }/p$}
25.3 1982. 366-370.
Williams, Hugh
.
A class of primality tests for trinomials which includes the {L}ucas-{L}ehmer test
98.2 1982. 477-494.
Williams, Hugh
.
Corrigendum: ``{S}ome primes with interesting digit patterns'' [{M}ath. {C}omp. {\bf 32} (1978), no. 144, 1306-1310;\ {MR} {\bf 58} \#484]
39.160 1982. 759.
Baillie, Robert , Cormack, G. and
Williams, Hugh
.
Corrigenda: ``{T}he problem of {S}ierpi\'nski concerning {$k\cdot 2\sp{n}+1$}'' [{M}ath. {C}omp. {\bf 37} (1981), no. 155, 229-231]
39.159 1982. 308.
Williams, Hugh
.
A {$p+1$} method of factoring
39.159 1982. 225-234.
Williams, Hugh
.
Determination of principal factors in {${\scr Q}(\sqrt{D})$} and {${\scr Q}(\root 3\of D)$}
38.157 1982. 261-274.
Williams, Hugh
.
The influence of computers in the development of number theory
8.2 1982. 75-93.
Shanks, Daniel and
Williams, Hugh
.
Gunderson's function in {F}ermat's last theorem
36.153 1981. 291-295.
Baillie, Robert , Cormack, G. and
Williams, Hugh
.
The problem of {S}ierpi\'nski concerning {$k\cdot 2\sp{n}+1$}
37.155 1981. 229-231.
Williams, Hugh
.
Some results concerning {V}orono\u\i 's continued fraction over {${\bf Q}(\root 3\of{D})$}
36.154 1981. 631-652.
Williams, Hugh
.
A numerical investigation into the length of the period of the continued fraction expansion of {$\sqrt{D}$}
36.154 1981. 593-601.
Williams, Hugh
.
The primality of certain integers of the form {$2Ar\sp{n}-1$}
39.1 1981. 7-17.
Newman, Morris , Shanks, Daniel and
Williams, Hugh
.
Simple groups of square order and an interesting sequence of primes
38.2 1980/81. 129-140.
Williams, Hugh
.
Improving the speed of calculating the regulator of certain pure cubic fields
35.152 1980. 1423-1434.
Cormack, G. V. and
Williams, Hugh
.
Some very large primes of the form {$k\cdot 2\sp{m}+1$}
35.152 1980. 1419-1421.
Williams, Hugh
, Cormack, G. and Seah, E.
.
Calculation of the regulator of a pure cubic field
34.150 1980. 567-611.
Williams, Hugh
.
Some results concerning the nearest integer continued fraction expansion of {$\surd D$}
315. 1980. 1-15.
Williams, Hugh
.
A modification of the {RSA} public-key encryption procedure
26.6 1980. 726-729.
Purdy, G. , Terras, R. , Terras, A. and
Williams, Hugh
.
Graphing {$L$}-functions of {K}ronecker symbols in the real part of the critical strip
47.2-4 1979. 101-131 (1985).
Williams, Hugh
and Shanks, Daniel
.
A note on class-number one in pure cubic fields
33.148 1979. 1317-1320.
Williams, Hugh
and Buhr, P. A.
.
Calculation of the regulator of {${\bf Q}(\surd D)$} by use of the nearest integer continued fraction algorithm
33.145 1979. 369-381.
Williams, Hugh
.
Errata: ``{C}ertain pure cubic fields with class-number one'' [{M}ath. {C}omp. {\bf 31} (1977), no. 138, 578-580;\ {MR} {\bf 55} \#5578]
33.146 1979. 847-848.
Diaz, F. , Shanks, Daniel and
Williams, Hugh
.
Quadratic fields with {$3$}-rank equal to {$4$}
33.146 1979. 836-840.
Williams, Hugh
and Seah, E.
.
Some primes of the form {$(a\sp{n}-1)/(a-1)$}
33.148 1979. 1337-1342.
Williams, Hugh
and Schmid, B.
.
Some remarks concerning the {M}.{I}.{T}. public-key cryptosystem
19.4 1979. 525-538.
Williams, Hugh
.
Some properties of a special set of recurring sequences
77.1 1978. 273-285.
Williams, Hugh
.
Some primes with interesting digit patterns
32.144 1978. 1306-1310.
Williams, Hugh
and Holte, R.
.
Some observations on primality testing
32.143 1978. 905-917.
Williams, Hugh
.
Primality testing on a computer
5. 1978. 127-185.
Williams, Hugh
.
On numbers analogous to the {C}armichael numbers
20.1 1977. 133-143.
Williams, Hugh
.
Certain pure cubic fields with class-number one
31.138 1977. 578-580.
Buell, D. A.,
Williams, Hugh
and Williams, K. S.
.
On the imaginary bicyclic biquadratic fields with class-number {$2$}
31.140 1977. 1034-1042.
Matthew, G. and
Williams, Hugh
.
Some new primes of the form {$k\cdot 2\sp{n}+1$}
31.139 1977. 797-798.
Williams, Hugh
and Holte, R.
.
Computation of the solution of {$x\sp{3}+Dy\sp{3}=1$}
31.139 1977. 778-785.
Williams, Hugh
.
Properties of some functions similar to {L}ucas functions
15.2 1977. 97-112.
Williams, Hugh
.
Some results on fundamental units in cubic fields
286/287. 1976. 75-85.
Stanton, R. G., Sudler, Jr. and
Williams, Hugh
.
An upper bound for the period of the simple continued fraction for {$\sqrt{D}$}
67.2 1976. 525-536.
Williams, Hugh
and Broere, J.
.
A computational technique for evaluating {$L(1,\chi )$} and the class number of a real quadratic field
30.136 1976. 887-893.
Williams, Hugh
and Judd, J. S.
.
Some algorithms for prime testing using generalized {L}ehmer functions
30.136 1976. 867-886.
Williams, Hugh
and Judd, J. S.
.
Determination of the primality of {$N$} by using factors of {$N\sp{2}\pm 1$}
30.133 1976. 157-172.
Barrucand, Pierre ,
Williams, Hugh
and Baniuk, L.
.
A computational technique for determining the class number of a pure cubic field
30.134 1976. 312-323.
Williams, Hugh
.
A generalization of {L}ehmer's functions
29.4 1976. 315-341.
Stanton, R. G. and
Williams, Hugh
.
An application of combinatorics in number theory
1.1 1976. 321-330.
Williams, Hugh
.
The rank of apparition of a generalized {F}ibonacci sequence
13.3 1975. 240-242.
Williams, Hugh
.
On {F}ibonacci numbers of the form {$k\sp{2}+1$}
13.3 1975. 213-214.
Williams, Hugh
and Zarnke, C. R.
.
Some algorithms for solving a cubic congruence modulo {$p$}
6. 1974. 285-306.
Williams, Hugh
.
The quadratic character of a certain quadratic surd
5. 1974. 49-55.
Williams, Hugh
and Zarnke, C. R.
.
Computer calculation of units in cubic fields
1973. 433-468. Congressus Numerantium, No. VII.
Williams, Hugh
and Zarnke, C. R.
.
Computer solution of the {D}iophantine equation {$x\sp{2}-dy\sp{4}=-1$}
1973. 405-416. Congressus Numerantium, No. VII.
Williams, Hugh
and Zarnke, C. R.
.
Computation of the solutions of the {D}iophantine equation {$x\sp{2}-dy\sp{4}=1$}
1972. 463-483.
Beach, B. D. and
Williams, Hugh
.
A numerical investigation of the {D}iophantine equation {$x\sp{2}-dy\sp{2}=-1$}
1972. 37-68.
Williams, Hugh
.
Some algorithms for solving {$x\sp{q}\equiv N$} {$({\rm mod}\ p)$}
1972. 451-462.
Williams, Hugh
.
The primality of {$N=2A3\sp{n}-1$}
15. 1972. 585-589.
Williams, Hugh
and Zarnke, C. R.
.
Some prime numbers of the forms {$2A3\sp{n}+1$} and {$2A3\sp{n}-1$}
26. 1972. 995-998.
Williams, Hugh
.
On a generalization of the {L}ucas functions
20. 1972. 33-51.
Williams, Hugh
.
Fibonacci numbers obtained from {P}ascal's triangle with generalizations
10.4 1972. 405-412.
Williams, Hugh
.
An algorithm for determining certain large primes
1971. 533-556.
Gryte, D. G., Kingsley, R. A. and
Williams, Hugh
.
On certain forms of {F}ibonacci numbers
1971. 339-344.
Beach, B. D. and
Williams, Hugh
.
Some computer results on periodic continued fractions
1971. 133-146.
Beach, B. D.,
Williams, Hugh
and Zarnke, C. R.
.
Some computer results on units in quadratic and cubic fields
1971. 609-648.
Williams, Hugh
and Zarnke, C. R.
.
Computation of the solutions of the {D}iophantine equation {$x\sp{3}+dy\sp{3}=1$}
1971. 671-676.
Beach, B. D. and
Williams, Hugh
.
A computer algorithm for determining the solution of the {D}iophantine equation {$x\sp{4}-dy\sp{4}=1$}
1971. 663-670. Dept. Comput. Sci., Univ.
Williams, Hugh
.
Some properties of the general {L}ucas polynomials
21. 1971. 91-93, 82.
Williams, Hugh
.
Note on a diophantine equation
25. 1970. 123-125.
Williams, Hugh
and Zarnke, C. R.
.
A report on prime numbers of the forms {$M=(6a+1)2\sp{2m-1}-1$} and {$M\sp{\prime} =(6a-1)2\sp{2m}-1$}
22. 1968. 420-422.
Stanton, R. G.,
Williams, Hugh
and Zarnke, C. R.
.
A packing problem
10. 1967. 287-297.
Courses
Supervised Students
Research Groups
ISPIA
Degrees
1966 - B.Sc. (Honours) -
University of Waterloo
1967 - M.Math -
University of Waterloo
1969 - Ph.D. -
University of Waterloo
Students
Ph.D. Students:
Alan Silvester
2007 to Present
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