Jacobson, M. J. jun.; Williams, H. C.; Wooding, K. Imaginary cyclic quartic fields with large minus class numbers. (English) Zbl 1125.11350 Buell, Duncan (ed.), Algorithmic number theory. 6th international symposium, ANTS-VI, Burlington, VT, USA, June 13–18, 2004. Proceedings. Berlin: Springer (ISBN 3-540-22156-5/pbk). Lecture Notes in Computer Science 3076, 280-292 (2004). MSC: 11R29 11Y40 11R16 11-04 PDFBibTeX XMLCite \textit{M. J. Jacobson jun.} et al., Lect. Notes Comput. Sci. 3076, 280--292 (2004; Zbl 1125.11350) Full Text: DOI
van der Poorten, A. J.; te Riele, H. J. J.; Williams, H. C. Computer verification of the Ankeny-Artin-Chowla Conjecture for all primes less than \(100 000 000 000\). (English) Zbl 0987.11065 Math. Comput. 70, No. 235, 1311-1328 (2001); corrigenda and addition ibid. 72, No. 241, 521-523 (2003). Reviewer: Tauno Metsänkylä (Turku) MSC: 11R11 11-04 11Y40 11Y65 11A55 11J70 PDFBibTeX XMLCite \textit{A. J. van der Poorten} et al., Math. Comput. 70, No. 235, 1311--1328 (2001; Zbl 0987.11065) Full Text: DOI
Lukes, Richard F.; Scheidler, Renate; Williams, Hugh C. Further tabulation of the Erdős-Selfridge function. (English) Zbl 0886.11051 Math. Comput. 66, No. 220, 1709-1717 (1997). MSC: 11N25 11Y70 11-04 11N36 PDFBibTeX XMLCite \textit{R. F. Lukes} et al., Math. Comput. 66, No. 220, 1709--1717 (1997; Zbl 0886.11051) Full Text: DOI
Lukes, R. F.; Patterson, C. D.; Williams, H. C. Some results on pseudosquares. (English) Zbl 0852.11072 Math. Comput. 65, No. 213, 361-372, S25-S27 (1996). Reviewer: H.J.Godwin (Egham) MSC: 11Y11 11A51 11-04 11Y35 11M20 11M26 PDFBibTeX XMLCite \textit{R. F. Lukes} et al., Math. Comput. 65, No. 213, 361--372, S25--S27 (1996; Zbl 0852.11072) Full Text: DOI
Williams, Hugh Number theory and finite fields. (English) Zbl 0911.11002 Colbourn, Charles J. (ed.) et al., The CRC handbook of combinatorial designs. Boca Raton, FL: CRC Press. CRC Press Series on Discrete Mathematics and its Applications. 615-644 (1996). MSC: 11-04 11A15 11A41 11A51 11T06 11T22 11Y70 PDFBibTeX XMLCite \textit{H. Williams}, in: The CRC handbook of combinatorial designs. Boca Raton, FL: CRC Press. 615--644 (1996; Zbl 0911.11002)
Fung, G. W.; Williams, H. C. Errata: On the computation of a table of complex cubic fields with discriminant \(D> -10^ 6\). (English) Zbl 0835.11041 Math. Comput. 63, No. 207, 433 (1994). MSC: 11R16 11-04 11R29 11Y40 PDFBibTeX XMLCite \textit{G. W. Fung} and \textit{H. C. Williams}, Math. Comput. 63, No. 207, 433 (1994; Zbl 0835.11041) Full Text: DOI
Scheidler, Renate; Williams, Hugh C. A method of tabulating the number-theoretic function \(g(k)\). (English) Zbl 0761.11037 Math. Comput. 59, No. 199, 251-257 (1992). Reviewer: M.Nair (Glasgow) MSC: 11N25 11Y70 11-04 PDFBibTeX XMLCite \textit{R. Scheidler} and \textit{H. C. Williams}, Math. Comput. 59, No. 199, 251--257 (1992; Zbl 0761.11037) Full Text: DOI
Buchmann, J.; Sands, J. W.; Williams, H. C. \(p\)-adic computation of real quadratic class numbers. (English) Zbl 0699.12007 Math. Comput. 54, No. 190, 855-868 (1990). Reviewer: Richard A. Mollin (Calgary) MSC: 11R11 11-04 11R29 11Y40 PDFBibTeX XMLCite \textit{J. Buchmann} et al., Math. Comput. 54, No. 190, 855--868 (1990; Zbl 0699.12007) Full Text: DOI
Stephens, A. J.; Williams, H. C. Some computational results on a problem of Eisenstein. (English) Zbl 0689.10024 Théorie des nombres, C. R. Conf. Int., Québec/Can. 1987, 869-886 (1989). Reviewer: M. D. Hendy (Palmerston North) MSC: 11Y65 11Y50 11-04 11D04 PDFBibTeX XML
Buchmann, Johannes; Williams, H. C. On the infrastructure of the principal ideal class of an algebraic number field of unit rank one. (English) Zbl 0653.12005 Math. Comput. 50, No. 182, 569-579 (1988). Reviewer: K.Peeva MSC: 11R52 12-04 PDFBibTeX XMLCite \textit{J. Buchmann} and \textit{H. C. Williams}, Math. Comput. 50, No. 182, 569--579 (1988; Zbl 0653.12005) Full Text: DOI
Dueck, G.; Williams, H. C. Corrigendum to: “Computation of the class number and class group of a complex cubic field”. (English) Zbl 0652.12003 Math. Comput. 50, No. 182, 223-231 (1988). Reviewer: K.Lakkis MSC: 11R16 11R23 12-04 68Q25 12D99 PDFBibTeX XMLCite \textit{G. Dueck} and \textit{H. C. Williams}, Math. Comput. 50, No. 182, 223--231 (1988; Zbl 0652.12003)
Stephens, A. J.; Williams, H. C. Some computational results on a problem concerning powerful numbers. (English) Zbl 0642.12001 Math. Comput. 50, No. 182, 619-632 (1988). Reviewer: R.Mollin MSC: 12-04 11R23 11R11 11B39 PDFBibTeX XMLCite \textit{A. J. Stephens} and \textit{H. C. Williams}, Math. Comput. 50, No. 182, 619--632 (1988; Zbl 0642.12001) Full Text: DOI
Buchmann, Johannes; Williams, H. C. On principal ideal testing in totally complex quartic fields and the determination of certain cyclotomic constants. (English) Zbl 0626.12006 Math. Comput. 48, 55-66 (1987). Reviewer: M.Pohst MSC: 11R16 11H06 12-04 11T22 11R18 PDFBibTeX XMLCite \textit{J. Buchmann} and \textit{H. C. Williams}, Math. Comput. 48, 55--66 (1987; Zbl 0626.12006) Full Text: DOI
Buchmann, Johannes; Williams, H. C. On principal ideal testing in algebraic number fields. (English) Zbl 0624.12007 J. Symb. Comput. 4, 11-19 (1987). Reviewer: K.S.Williams MSC: 11R21 11T22 12-04 PDFBibTeX XMLCite \textit{J. Buchmann} and \textit{H. C. Williams}, J. Symb. Comput. 4, 11--19 (1987; Zbl 0624.12007) Full Text: DOI
Williams, H. C.; Wunderlich, M. C. On the parallel generation of the residues for the continued fraction factoring algorithm. (English) Zbl 0617.10005 Math. Comput. 48, 405-423 (1987). Reviewer: M.D.Hendy MSC: 11Y05 11A55 11-04 68W10 PDFBibTeX XMLCite \textit{H. C. Williams} and \textit{M. C. Wunderlich}, Math. Comput. 48, 405--423 (1987; Zbl 0617.10005) Full Text: DOI
Williams, H. C. Effective primality tests for some integers of the forms \(A5^ n-1\) and \(A7^ n-1\). (English) Zbl 0608.10003 Math. Comput. 48, 385-403 (1987). MSC: 11-04 11A41 11B37 PDFBibTeX XMLCite \textit{H. C. Williams}, Math. Comput. 48, 385--403 (1987; Zbl 0608.10003) Full Text: DOI
Williams, H. C. The spacing of the minima in certain cubic lattices. (English) Zbl 0615.12003 Pac. J. Math. 124, 483-496 (1986). Reviewer: C.Levesque MSC: 12-04 11J70 11R16 11R27 PDFBibTeX XMLCite \textit{H. C. Williams}, Pac. J. Math. 124, 483--496 (1986; Zbl 0615.12003) Full Text: DOI
Williams, H. C. Primality testing on a computer. (Russian) Zbl 0607.10004 Kibern. Sb., Nov. Ser. 23, 61-99 (1986). MSC: 11A41 11-04 PDFBibTeX XMLCite \textit{H. C. Williams}, Kibern. Sb., Nov. Ser. 23, 61--99 (1986; Zbl 0607.10004)
Williams, H. C.; Dubner, Harvey The primality of R1031. (English) Zbl 0602.10001 Math. Comput. 47, 703-711 (1986). Reviewer: O.Ninnemann MSC: 11-04 11A41 PDFBibTeX XMLCite \textit{H. C. Williams} and \textit{H. Dubner}, Math. Comput. 47, 703--711 (1986; Zbl 0602.10001) Full Text: DOI
Kurtz, G. C.; Shanks, Daniel; Williams, H. C. Fast primality tests for numbers less than 50 \(\cdot \,10^ 9\). (English) Zbl 0594.10001 Math. Comput. 46, 691-701 (1986). Reviewer: H.J.J.te Riele MSC: 11-04 11A41 11B37 PDFBibTeX XMLCite \textit{G. C. Kurtz} et al., Math. Comput. 46, 691--701 (1986; Zbl 0594.10001) Full Text: DOI
Tennenhouse, M.; Williams, H. C. A note on class-number one in certain real quadratic and pure cubic fields. (English) Zbl 0589.12003 Math. Comput. 46, 333-336 (1986). Reviewer: V.Ennola MSC: 12-04 11R11 11R16 11R23 PDFBibTeX XMLCite \textit{M. Tennenhouse} and \textit{H. C. Williams}, Math. Comput. 46, 333--336 (1986; Zbl 0589.12003) Full Text: DOI
Dueck, G.; Williams, H. C. Computation of the class number and class group of a complex cubic field. (English) Zbl 0576.12006 Math. Comput. 45, 223-231 (1985). Reviewer: H.J.Godwin MSC: 11R16 11R23 12-04 68Q25 PDFBibTeX XMLCite \textit{G. Dueck} and \textit{H. C. Williams}, Math. Comput. 45, 223--231 (1985; Zbl 0576.12006) Full Text: DOI
Patterson, C. D.; Williams, H. C. Some periodic continued fractions with long periods. (English) Zbl 0565.10008 Math. Comput. 44, 523-532 (1985). Reviewer: H.Jager MSC: 11A55 11-04 11R11 11R16 PDFBibTeX XMLCite \textit{C. D. Patterson} and \textit{H. C. Williams}, Math. Comput. 44, 523--532 (1985; Zbl 0565.10008) Full Text: DOI
Williams, H. C. Factoring on a computer. (English) Zbl 0548.10004 Math. Intell. 6, No. 3, 29-36 (1984). Reviewer: H. J. Godwin (Egham) MSC: 11Y05 11Y16 11-02 11-04 PDFBibTeX XMLCite \textit{H. C. Williams}, Math. Intell. 6, No. 3, 29--36 (1984; Zbl 0548.10004) Full Text: DOI
Patterson, C. D.; Williams, H. C. A report on the University of Manitoba sieve unit. (English) Zbl 0539.10003 Numerical mathematics and computing, Proc. 12th Manitoba Conf., Winnipeg/Manit. 1982, Congr. Numerantium 37, 85-98 (1983). Reviewer: H.J.Godwin MSC: 11A07 11-04 PDFBibTeX XML
Williams, H. C.; Dueck, G. W.; Schmid, B. K. A rapid method of evaluating the regulator and class number of a pure cubic field. (English) Zbl 0528.12004 Math. Comput. 41, 235-286 (1983). MSC: 11R16 11R27 11R23 12-04 PDFBibTeX XMLCite \textit{H. C. Williams} et al., Math. Comput. 41, 235--286 (1983; Zbl 0528.12004) Full Text: DOI
Williams, H. C. Corrigendum. Some primes with interesting digit patterns. (English) Zbl 0506.10008 Math. Comput. 39, 759 (1982). MSC: 11A41 11-04 PDFBibTeX XMLCite \textit{H. C. Williams}, Math. Comput. 39, 759 (1982; Zbl 0506.10008) Full Text: DOI
Baillie, Robert; Cormack, G.; Williams, H. C. Corrigenda. “The problem of Sierpinski concerning \(k\cdot 2^n+1\)”. (English) Zbl 0495.10003 Math. Comput. 39, 308 (1982). MSC: 11-04 11A41 PDFBibTeX XMLCite \textit{R. Baillie} et al., Math. Comput. 39, 308 (1982; Zbl 0495.10003) Full Text: DOI
Williams, H. C. Determination of principal factors in \(Q(\sqrt{D})\) and \(Q(D^{1/3})\). (English) Zbl 0491.12006 Math. Comput. 38, 261-274 (1982). MSC: 11R23 11R11 11R16 12-04 PDFBibTeX XMLCite \textit{H. C. Williams}, Math. Comput. 38, 261--274 (1982; Zbl 0491.12006) Full Text: DOI
Williams, H. C. The influence of computers in the development of number theory. (English) Zbl 0486.10001 Comput. Math. Appl. 8, 75-93 (1982). MSC: 11-02 11-03 11-04 12-04 68Q25 11A41 11A63 11D41 11N05 11M06 11R27 11R23 PDFBibTeX XMLCite \textit{H. C. Williams}, Comput. Math. Appl. 8, 75--93 (1982; Zbl 0486.10001) Full Text: DOI
Williams, H. C. Some results concerning Voronoi’s continued fraction over \(Q(D^{1/3})\). (English) Zbl 0486.12002 Math. Comput. 36, 631-652 (1981). MSC: 11R16 11R23 11R27 12-04 PDFBibTeX XMLCite \textit{H. C. Williams}, Math. Comput. 36, 631--652 (1981; Zbl 0486.12002) Full Text: DOI
Williams, H. C. A numerical investigation into the length of the period of the continued fraction expansion of \(\sqrt D\). (English) Zbl 0476.10008 Math. Comput. 36, 593-601 (1981). Reviewer: H. J. Godwin (Egham) MSC: 11Y55 11-04 11A55 PDFBibTeX XMLCite \textit{H. C. Williams}, Math. Comput. 36, 593--601 (1981; Zbl 0476.10008) Full Text: DOI
Baillie, Robert; Cormack, G.; Williams, H. C. The problem of Sierpiński concerning \(k\cdot 2^n+1\). (English) Zbl 0472.10008 Math. Comput. 37, 229-231 (1981). Reviewer: H. J. Godwin (Egham) MSC: 11A41 11-04 11A51 PDFBibTeX XMLCite \textit{R. Baillie} et al., Math. Comput. 37, 229--231 (1981; Zbl 0472.10008) Full Text: DOI
Shanks, Daniel; Williams, H. C. Gunderson’s function in Fermat’s last theorem. (English) Zbl 0452.10002 Math. Comput. 36, 291-295 (1981). MSC: 11A25 11D41 11-04 PDFBibTeX XMLCite \textit{D. Shanks} and \textit{H. C. Williams}, Math. Comput. 36, 291--295 (1981; Zbl 0452.10002) Full Text: DOI
Williams, H. C. Improving the speed of calculating the regulator of certain pure cubic fields. (English) Zbl 0455.12005 Math. Comput. 35, 1423-1434 (1980). MSC: 11R23 11R16 12-04 PDFBibTeX XMLCite \textit{H. C. Williams}, Math. Comput. 35, 1423--1434 (1980; Zbl 0455.12005) Full Text: DOI
Cormack, G. V.; Williams, H. C. Some very large primes of the form \(k\cdot 2^m+1\). (English) Zbl 0443.10004 Math. Comput. 35, 1419-1421 (1980). MSC: 11A41 11B39 11-04 PDFBibTeX XMLCite \textit{G. V. Cormack} and \textit{H. C. Williams}, Math. Comput. 35, 1419--1421 (1980; Zbl 0443.10004) Full Text: DOI
Williams, H. C.; Cormack, G.; Seah, E. Calculation of the regulator of a pure cubic field. (English) Zbl 0431.12006 Math. Comput. 34, 567-611 (1980). MSC: 11R27 11R16 12-04 PDFBibTeX XMLCite \textit{H. C. Williams} et al., Math. Comput. 34, 567--611 (1980; Zbl 0431.12006) Full Text: DOI
Williams, H. C.; Seah, E. Some primes of the form \((a^n-1)/(a-1)\). (English) Zbl 0417.10004 Math. Comput. 33, 1337-1342 (1979). MSC: 11A41 11-04 PDFBibTeX XMLCite \textit{H. C. Williams} and \textit{E. Seah}, Math. Comput. 33, 1337--1342 (1979; Zbl 0417.10004) Full Text: DOI
Diaz y Diaz, Francisco; Shanks, Daniel; Williams, H. C. Quadratic fields with 3-rank equal to 4. (English) Zbl 0409.12009 Math. Comput. 33, 836-840 (1979). MSC: 11R23 12-04 11R11 PDFBibTeX XMLCite \textit{F. Diaz y Diaz} et al., Math. Comput. 33, 836--840 (1979; Zbl 0409.12009) Full Text: DOI
Williams, H. C. Primality testing on a computer. (English) Zbl 0406.10008 Ars Comb. 5, 127-185 (1978). MSC: 11A41 11-04 PDFBibTeX XMLCite \textit{H. C. Williams}, Ars Comb. 5, 127--185 (1978; Zbl 0406.10008)
Williams, H. C. Some primes with interesting digit patterns. (English) Zbl 0388.10007 Math. Comput. 32, 1306-1310 (1978). MSC: 11A41 11-04 11A63 PDFBibTeX XMLCite \textit{H. C. Williams}, Math. Comput. 32, 1306--1310 (1978; Zbl 0388.10007) Full Text: DOI
Williams, H. C.; Holte, R. Some observations on primality testing. (English) Zbl 0382.10005 Math. Comput. 32, 905-917 (1978). MSC: 11A41 11-04 PDFBibTeX XMLCite \textit{H. C. Williams} and \textit{R. Holte}, Math. Comput. 32, 905--917 (1978; Zbl 0382.10005) Full Text: DOI
Matthew, G.; Williams, H. C. Some new primes of the form \(k2^2+1\). (English) Zbl 0376.10002 Math. Comput. 31, 797-798 (1977). MSC: 11-04 11A41 11B39 PDFBibTeX XMLCite \textit{G. Matthew} and \textit{H. C. Williams}, Math. Comput. 31, 797--798 (1977; Zbl 0376.10002) Full Text: DOI
Williams, H. C.; Broere, J. A computational technique for evaluating \(L(1,\chi)\) and the class number of a real quadratic field. (English) Zbl 0345.12004 Math. Comput. 30, 887-893 (1976). MSC: 11R11 11R23 11R42 12-04 PDFBibTeX XMLCite \textit{H. C. Williams} and \textit{J. Broere}, Math. Comput. 30, 887--893 (1976; Zbl 0345.12004) Full Text: DOI
Barrucand, Pierre; Williams, H. C.; Baniuk, L. A computational technique for determining the class number of a pure cubic field. (English) Zbl 0324.12005 Math. Comput. 30, 312-323 (1976). MSC: 11R23 11R16 12-04 11R42 PDFBibTeX XMLCite \textit{P. Barrucand} et al., Math. Comput. 30, 312--323 (1976; Zbl 0324.12005) Full Text: DOI
Williams, H. C.; Zarnke, C. R. Some algorithms for solving a cubic congruence modulo \(p\). (English) Zbl 0294.10001 Util. Math. 6, 285-306 (1974). Reviewer: R. Finkelstein (R. P. Steiner) MSC: 11A07 11-04 PDFBibTeX XMLCite \textit{H. C. Williams} and \textit{C. R. Zarnke}, Util. Math. 6, 285--306 (1974; Zbl 0294.10001)
Williams, H. C.; Zarnke, C. R. Computer calculation of units in cubic fields. (English) Zbl 0312.12012 Proc. 2nd Manit. Conf. numer. Math., Winnipeg 1972, 433-468 (1973). Reviewer: R. P. Steiner MSC: 11Y40 11R27 11R16 11-04 PDFBibTeX XML
Williams, H. C.; Zarnke, C. R. Computer solution of the Diophantine equation \(x^2-dy^4=-1\). (English) Zbl 0311.10024 Proc. 2nd Manit. Conf. numer. Math., Winnipeg 1972, 405-416 (1973). MSC: 11D25 11-04 PDFBibTeX XML
Williams, H. C.; Zarnke, C. R. Computation of the solutions of the Diophantine equation \(x^2-dy^2=1\). (English) Zbl 0261.10016 Proc. 3rd Southeast. Conf. Combinat., Graph Theory, Computing, Florida Atlantic Univ., Boca Raton 1972, 463-483 (1972). MSC: 11-04 11D25 PDFBibTeX XML
Beach, B. D.; Williams, H. C. A numerical investigation of the Diophantine equation \(x^2-dy^2=-1\). (English) Zbl 0261.10015 Proc. 3rd Southeast. Conf. Combinat., Graph Theory, Computing, Florida Atlantic Univ., Boca Raton 1972, 37-68 (1972). MSC: 11-04 11D04 PDFBibTeX XML
Beach, B. D.; Williams, H. C.; Zarnke, C. R. Some computer results on units in quadratic and cubic fields. (English) Zbl 0348.12003 Proc. 25th Summer Meet. Can. math. Congr., Thunder Bay 1971, 609-648 (1971). MSC: 11R11 12-04 11H99 11E76 11R27 11R16 PDFBibTeX XML
Zarnke, C. R.; Williams, H. C. Computer determination of some large primes. (English) Zbl 0295.10001 Proc. 2nd Louisiana Conf. Combin., Graph Theory, Computing; Baton Rouge, 563-570 (1971). MSC: 11-04 11A41 PDFBibTeX XML
Gryte, D. G.; Kingsley, R. A.; Williams, H. C. On certain forms of Fibonacci numbers. (English) Zbl 0293.10002 Proc. 2nd Louisiana Conf. Combin., Graph Theory, Computing; Baton Rouge, 339-344 (1971). MSC: 11-04 11D41 11B37 PDFBibTeX XML
Beach, B. D.; Williams, H. C. Some computer results on periodic conti ued fractions. (English) Zbl 0291.10001 Proc. 2nd Louisiana Conf. Combin., Graph Theory, Computing; Baton Rouge, 133-146 (1971). MSC: 11-04 11A63 PDFBibTeX XML
Beach, B. D.; Williams, H. C. A computer algorithm for determining the solution of the Diophantine equation \(x^4-dy^4=1\). (English) Zbl 0265.10010 Proc. Manitoba Conf. numer. Math. 1971, 663-670 (1971). MSC: 11D25 11-04 PDFBibTeX XML
Williams, H. C.; Zarnke, C. R. Computation of the solutions of the Diophantine equation \(x^3+dy^3=1\). (English) Zbl 0265.10009 Proc. Manitoba Conf. numer. Math. 1971, 671-676 (1971). MSC: 11D25 11-04 PDFBibTeX XML
Williams, H. C.; Zarnke, C. R. A report on prime numbers of the forms \(M =(6a+1) 2^{2n-1}-1\) and \(M' =(6a-1) 2^{2n} -1\). (English) Zbl 0157.08701 Math. Comput. 22, 420-422 (1968). Reviewer: Hugh C. Williams (Winnipeg) MSC: 11-04 11A41 PDFBibTeX XMLCite \textit{H. C. Williams} and \textit{C. R. Zarnke}, Math. Comput. 22, 420--422 (1968; Zbl 0157.08701) Full Text: DOI