Bugeaud, Yann On the size of integer solutions of elliptic equations. II. (English) Zbl 1185.11018 Bull. Greek Math. Soc. 43, 125-130 (2000). Reviewer: Florin Nicolae (Berlin) MSC: 11D25 11G05 PDFBibTeX XMLCite \textit{Y. Bugeaud}, Bull. Greek Math. Soc. 43, 125--130 (2000; Zbl 1185.11018) Full Text: EuDML
Brown, Ezra Three Fermat trails to elliptic curves. (English) Zbl 0995.11514 Coll. Math. J. 31, No. 3, 162-172 (2000). MSC: 11D25 11G05 PDFBibTeX XMLCite \textit{E. Brown}, Coll. Math. J. 31, No. 3, 162--172 (2000; Zbl 0995.11514) Full Text: DOI
Kuba, G.; Müller, Helmut; Nowak, W. G.; Schoissengeier, J. On the distribution of the power of integers of a complex cubic number field. (Zur Verteilung der Potenzen ganzer Zahlen eines komplexen kubischen Zahlkörpers.) (German) Zbl 1008.11039 Abh. Math. Semin. Univ. Hamb. 70, 341-354 (2000). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11R16 11P21 11R04 11R47 PDFBibTeX XMLCite \textit{G. Kuba} et al., Abh. Math. Semin. Univ. Hamb. 70, 341--354 (2000; Zbl 1008.11039) Full Text: DOI
Qiu, Derong; Zhang, Xianke Elliptic curves of twin primes over the Gaussian field and Diophantine equations. (English) Zbl 1037.11502 Adv. Math., Beijing 29, No. 3, 279-281 (2000). MSC: 11G05 11D25 PDFBibTeX XMLCite \textit{D. Qiu} and \textit{X. Zhang}, Adv. Math., Beijing 29, No. 3, 279--281 (2000; Zbl 1037.11502) Full Text: arXiv
Scheidler, Renate Reduction in purely cubic function fields of unit rank one. (English) Zbl 1035.11057 Bosma, Wieb (ed.), Algorithmic number theory. 4th international symposium. ANTS-IV, Leiden, the Netherlands, July 2–7, 2000. Proceedings. Berlin: Springer (ISBN 3-540-67695-3). Lect. Notes Comput. Sci. 1838, 515-532 (2000). Reviewer: Robert F. Lax (Baton Rouge) MSC: 11R58 11Y16 11R16 14H05 PDFBibTeX XMLCite \textit{R. Scheidler}, Lect. Notes Comput. Sci. 1838, 515--532 (2000; Zbl 1035.11057)
Cohen, Henri; Diaz y Diaz, Francisco; Olivier, Michel Counting discriminants of number fields of degree up to four. (English) Zbl 0987.11080 Bosma, Wieb (ed.), Algorithmic number theory. 4th international symposium. ANTS-IV, Leiden, the Netherlands, July 2-7, 2000. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1838, 269-283 (2000). Reviewer: M.Pohst (Berlin) MSC: 11Y40 11R16 11R11 11-04 PDFBibTeX XMLCite \textit{H. Cohen} et al., Lect. Notes Comput. Sci. 1838, 269--283 (2000; Zbl 0987.11080)
Cohen, Henri; Diaz y Diaz, Francisco; Olivier, Michel Construction of tables of quartic number fields. (English) Zbl 0987.11079 Bosma, Wieb (ed.), Algorithmic number theory. 4th international symposium. ANTS-IV, Leiden, the Netherlands, July 2-7, 2000. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1838, 257-268 (2000). Reviewer: M.Pohst (Berlin) MSC: 11Y40 11R16 11-04 PDFBibTeX XMLCite \textit{H. Cohen} et al., Lect. Notes Comput. Sci. 1838, 257--268 (2000; Zbl 0987.11079)
Bruin, Nils On powers as sums of two cubes. (English) Zbl 0986.11021 Bosma, Wieb (ed.), Algorithmic number theory. 4th international symposium. ANTS-IV, Leiden, the Netherlands, July 2-7, 2000. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1838, 169-184 (2000). Reviewer: Michael Stoll (Düsseldorf) MSC: 11D25 11Y50 11D41 14G05 14G25 PDFBibTeX XMLCite \textit{N. Bruin}, Lect. Notes Comput. Sci. 1838, 169--184 (2000; Zbl 0986.11021)
Kuwata, Masato; Top, Jaap A singular \(K3\) surface related to sums of consecutive cubes. (English) Zbl 0981.14014 Indag. Math., New Ser. 11, No. 3, 419-435 (2000). Reviewer: B.Kunyavskii (Ramat Gan) MSC: 14J28 11D25 14G25 11G99 PDFBibTeX XMLCite \textit{M. Kuwata} and \textit{J. Top}, Indag. Math., New Ser. 11, No. 3, 419--435 (2000; Zbl 0981.14014) Full Text: DOI arXiv
Kim, Hyun Kwang; Hwang, Hyung Ju Values of zeta functions and class number 1 criterion for the simplest cubic fields. (English) Zbl 0999.11067 Nagoya Math. J. 160, 161-180 (2000). Reviewer: Radan Kučera (Brno) MSC: 11R16 11R42 PDFBibTeX XMLCite \textit{H. K. Kim} and \textit{H. J. Hwang}, Nagoya Math. J. 160, 161--180 (2000; Zbl 0999.11067) Full Text: DOI
Zaharescu, Alexandru A metric symbol for pairs of polynomials over local fields. (English) Zbl 0972.11111 C. R. Math. Acad. Sci., Soc. R. Can. 22, No. 4, 147-150 (2000). Reviewer: Gabriel D.Villa-Salvador (México) MSC: 11S05 11D25 PDFBibTeX XMLCite \textit{A. Zaharescu}, C. R. Math. Acad. Sci., Soc. R. Can. 22, No. 4, 147--150 (2000; Zbl 0972.11111)
Dujella, Andrej Diophantine triples and construction of high-rank elliptic curves over \(\mathbb{Q}\) with three nontrivial 2-torsion points. (English) Zbl 0989.11032 Rocky Mt. J. Math. 30, No. 1, 157-164 (2000). Reviewer: Federico Pellarin (Caen) MSC: 11G05 11D25 PDFBibTeX XMLCite \textit{A. Dujella}, Rocky Mt. J. Math. 30, No. 1, 157--164 (2000; Zbl 0989.11032) Full Text: DOI arXiv Link
Kim, Jung Soo Efficient computation of rank of elliptic curves using hyperelliptic curves associated with the simplest cubic fields. (English) Zbl 0974.11025 Proc. Japan Acad., Ser. A 76, No. 9, 129-131 (2000). Reviewer: Amílcar Pacheco (Rio de Janeiro) MSC: 11G05 11R16 PDFBibTeX XMLCite \textit{J. S. Kim}, Proc. Japan Acad., Ser. A 76, No. 9, 129--131 (2000; Zbl 0974.11025) Full Text: DOI
Gaál, István; Pohst, Michael Computing power integral bases in quartic relative extensions. (English) Zbl 0993.11055 J. Number Theory 85, No. 2, 201-219 (2000). Reviewer: N.Tzanakis (Iraklion) MSC: 11R16 11R21 11Y50 PDFBibTeX XMLCite \textit{I. Gaál} and \textit{M. Pohst}, J. Number Theory 85, No. 2, 201--219 (2000; Zbl 0993.11055) Full Text: DOI Link
Swan, Richard G. Hilbert’s theorem on positive ternary quartics. (English) Zbl 1026.11045 Bayer-Fluckiger, Eva (ed.) et al., Quadratic forms and their applications. Proceedings of the conference, University College Dublin, Ireland, July 5-9, 1999. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 272, 287-292 (2000). Reviewer: N.Schwartz (Passau) MSC: 11E10 13J30 11E76 12D15 PDFBibTeX XMLCite \textit{R. G. Swan}, Contemp. Math. 272, 287--292 (2000; Zbl 1026.11045)
Powers, Victoria; Reznick, Bruce Notes towards a constructive proof of Hilbert’s theorem on ternary quartics. (English) Zbl 1026.11044 Bayer-Fluckiger, Eva (ed.) et al., Quadratic forms and their applications. Proceedings of the conference, University College Dublin, Ireland, July 5-9, 1999. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 272, 209-227 (2000). Reviewer: N.Schwartz (Passau) MSC: 11E10 13J30 11E76 PDFBibTeX XMLCite \textit{V. Powers} and \textit{B. Reznick}, Contemp. Math. 272, 209--227 (2000; Zbl 1026.11044)
Poulakis, Dimitrios; Voskos, Evaggelos On the practical solution of genus zero Diophantine equations. (English) Zbl 0985.11051 J. Symb. Comput. 30, No. 5, 573-582 (2000). Reviewer: Nikos Tzanakis (Iraklion) MSC: 11Y50 11R21 11D59 PDFBibTeX XMLCite \textit{D. Poulakis} and \textit{E. Voskos}, J. Symb. Comput. 30, No. 5, 573--582 (2000; Zbl 0985.11051) Full Text: DOI
Coward, Daniel R. Some sums of two rational cubes. (English) Zbl 0983.11030 Q. J. Math. 51, No. 4, 451-464 (2000). Reviewer: Roelof J.Stroeker (Rotterdam) MSC: 11G05 11D25 14G05 PDFBibTeX XMLCite \textit{D. R. Coward}, Q. J. Math. 51, No. 4, 451--464 (2000; Zbl 0983.11030) Full Text: DOI
Scheidler, R. Purely cubic complex function fields with small units. (English) Zbl 1160.11363 Acta Arith. 95, No. 4, 289-304 (2000). MSC: 11R58 11R16 11R27 14H05 PDFBibTeX XMLCite \textit{R. Scheidler}, Acta Arith. 95, No. 4, 289--304 (2000; Zbl 1160.11363) Full Text: DOI EuDML Link
Miura, Kei Field theory for function fields of singular plane quartic curves. (English) Zbl 0986.14016 Bull. Aust. Math. Soc. 62, No. 2, 193-204 (2000). Reviewer: Augusto Nobile (Baton Rouge) MSC: 14H05 14H20 12F20 PDFBibTeX XMLCite \textit{K. Miura}, Bull. Aust. Math. Soc. 62, No. 2, 193--204 (2000; Zbl 0986.14016) Full Text: DOI
Yoshida, Shin-ichi On the equation \(y^2=x^3+pqx\). (English) Zbl 0983.11033 Comment. Math. Univ. St. Pauli 49, No. 1, 23-42 (2000). Reviewer: Roelof J.Stroeker (Rotterdam) MSC: 11G05 14H52 11D25 PDFBibTeX XMLCite \textit{S.-i. Yoshida}, Comment. Math. Univ. St. Pauli 49, No. 1, 23--42 (2000; Zbl 0983.11033)
Azizi, Abdelmalek Capitulation of the 2-ideal classes of \(\mathbb{Q}(\sqrt{p_1p_2},i)\) where \(p_1\) and \(p_2\) are primes such that \(p_1\equiv 1 \pmod 8\), \(p_2\equiv 5 \pmod 8\) and \(\left(\frac{p_1}{p_2}\right)=-1\). (English) Zbl 1003.11050 Boulagouaz, M’hammed (ed.) et al., Algebra and number theory. Proceedings of a conference, Fez, Morocco. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 208, 13-19 (2000). Reviewer: Charles Parry (Blacksburg) MSC: 11R29 11R16 11R11 PDFBibTeX XMLCite \textit{A. Azizi}, Lect. Notes Pure Appl. Math. 208, 13--19 (2000; Zbl 1003.11050)
Dujella, Andrej; Pethő, Attila Integer points on a family of elliptic curves. (English) Zbl 0960.11019 Publ. Math. Debr. 56, No. 3-4, 321-335 (2000). MSC: 11D25 11G05 11D09 11Y50 PDFBibTeX XMLCite \textit{A. Dujella} and \textit{A. Pethő}, Publ. Math. Debr. 56, No. 3--4, 321--335 (2000; Zbl 0960.11019)
Pethő, Attila; Zimmer, Horst G. \(S\)-integer points on elliptic curves, theory and practice. (English) Zbl 0973.11107 Halter-Koch, Franz (ed.) et al., Algebraic number theory and diophantine analysis. Proceedings of the international conference, Graz, Austria, August 30-September 5, 1998. Berlin: Walter de Gruyter. 351-363 (2000). Reviewer: Roelof J.Stroeker (Rotterdam) MSC: 11Y50 11D25 11G05 PDFBibTeX XMLCite \textit{A. Pethő} and \textit{H. G. Zimmer}, in: Algebraic number theory and diophantine analysis. Proceedings of the international conference, Graz, Austria, August 30--September 5, 1998. Berlin: Walter de Gruyter. 351--363 (2000; Zbl 0973.11107)
Kida, Masanari Computing elliptic curves having good reduction everywhere over quadratic fields. II. (English) Zbl 1001.11024 Halter-Koch, Franz (ed.) et al., Algebraic number theory and Diophantine analysis. Proceedings of the international conference, Graz, Austria, August 30-September 5, 1998. Berlin: Walter de Gruyter. 239-247 (2000). Reviewer: Horst G.Zimmer (Saarbrücken) MSC: 11G05 11Y50 11D25 PDFBibTeX XMLCite \textit{M. Kida}, in: Algebraic number theory and diophantine analysis. Proceedings of the international conference, Graz, Austria, August 30--September 5, 1998. Berlin: Walter de Gruyter. 239--247 (2000; Zbl 1001.11024)
Cao, Zhenfu; Mu, Shanzhi; Dong, Xiaolei A new proof of a conjecture of Antoniadis. (English) Zbl 0958.11025 J. Number Theory 83, No. 2, 185-193 (2000). Reviewer: Jannis A.Antoniadis (Iraklion) MSC: 11D25 PDFBibTeX XMLCite \textit{Z. Cao} et al., J. Number Theory 83, No. 2, 185--193 (2000; Zbl 0958.11025) Full Text: DOI
Siksek, Samir The Hasse principle for a class of cubic surfaces. (English) Zbl 0962.11019 Arab J. Math. Sci. 6, No. 1, 85-87 (2000). Reviewer: D.Poulakis (Thessaloniki) MSC: 11D25 14G05 14J20 PDFBibTeX XMLCite \textit{S. Siksek}, Arab J. Math. Sci. 6, No. 1, 85--87 (2000; Zbl 0962.11019)
Otsubo, Noriyuki Selmer groups and zero-cycles on the Fermat quartic surface. (English) Zbl 1018.11033 J. Reine Angew. Math. 525, 113-146 (2000). Reviewer: O.Ninnemann (Berlin) MSC: 11G35 11G40 14C15 14C35 14G25 PDFBibTeX XMLCite \textit{N. Otsubo}, J. Reine Angew. Math. 525, 113--146 (2000; Zbl 1018.11033) Full Text: DOI
Rose, Harvey E. On some elliptic curves with large sha. (English) Zbl 0983.11032 Exp. Math. 9, No. 1, 85-89 (2000). Reviewer: Roelof J.Stroeker (Rotterdam) MSC: 11G05 14H52 11D25 PDFBibTeX XMLCite \textit{H. E. Rose}, Exp. Math. 9, No. 1, 85--89 (2000; Zbl 0983.11032) Full Text: DOI Euclid EuDML
Dujella, Andrej A parametric family of elliptic curves. (English) Zbl 0972.11048 Acta Arith. 94, No. 1, 87-101 (2000). Reviewer: Attila Pethő (Debrecen) MSC: 11G05 11Y50 11D25 PDFBibTeX XMLCite \textit{A. Dujella}, Acta Arith. 94, No. 1, 87--101 (2000; Zbl 0972.11048) Full Text: DOI EuDML
Kishi, Yasuhiro A constructive approach to Spiegelung relations between 3-ranks of absolute ideal class groups and congruent ones modulo \((3)^2\) in quadratic fields. (English) Zbl 0967.11048 J. Number Theory 83, No. 1, 1-49 (2000). Reviewer: Florence Soriano-Gafiuk (Schweyen) MSC: 11R37 11R29 11R16 11R70 11R11 PDFBibTeX XMLCite \textit{Y. Kishi}, J. Number Theory 83, No. 1, 1--49 (2000; Zbl 0967.11048) Full Text: DOI
Poulakis, Dimitrios Corrigendum to the paper “The number of solutions of the Mordell equation”. (English) Zbl 1016.11011 Acta Arith. 92, No. 4, 387-388 (2000). MSC: 11D25 11G05 PDFBibTeX XMLCite \textit{D. Poulakis}, Acta Arith. 92, No. 4, 387--388 (2000; Zbl 1016.11011) Full Text: DOI EuDML
Lemmermeyer, Franz Reciprocity laws. From Euler to Eisenstein. (English) Zbl 0949.11002 Springer Monographs in Mathematics. Berlin: Springer. xix, 487 p. (2000). Reviewer: Hans Opolka (Braunschweig) MSC: 11-03 11A15 01-01 11-01 11R18 11R37 PDFBibTeX XMLCite \textit{F. Lemmermeyer}, Reciprocity laws. From Euler to Eisenstein. Berlin: Springer (2000; Zbl 0949.11002)
Scheidler, R.; Stein, A. Voronoi’s algorithm in purely cubic congruence function fields of unit rank 1. (English) Zbl 1042.11068 Math. Comput. 69, No. 231, 1245-1266 (2000). MSC: 11R16 11R27 11R58 11-04 PDFBibTeX XMLCite \textit{R. Scheidler} and \textit{A. Stein}, Math. Comput. 69, No. 231, 1245--1266 (2000; Zbl 1042.11068) Full Text: DOI
Granville, Andrew; Stark, H. M. \(ABC\) implies no “Siegel zeros” for \(L\)-functions of characters with negative discriminant. (English) Zbl 0967.11033 Invent. Math. 139, No. 3, 509-523 (2000). Reviewer: Roger Heath-Brown (Oxford) MSC: 11M20 11D25 11R42 11F11 PDFBibTeX XMLCite \textit{A. Granville} and \textit{H. M. Stark}, Invent. Math. 139, No. 3, 509--523 (2000; Zbl 0967.11033) Full Text: DOI
Buchholz, Ralph H.; MacDougall, James A. When Newton met Diophantus: a study of rational-derived polynomials and their extension to quadratic fields. (English) Zbl 1035.11009 J. Number Theory 81, No. 2, 210-233 (2000). Reviewer: Horst G. Zimmer (Saarbrücken) MSC: 11D25 11D41 11C08 14H52 11R09 14J25 14J27 11G30 14H40 11G05 PDFBibTeX XMLCite \textit{R. H. Buchholz} and \textit{J. A. MacDougall}, J. Number Theory 81, No. 2, 210--233 (2000; Zbl 1035.11009) Full Text: DOI Link
Miura, Kei; Yoshihara, Hisao Field theory for function fields of plane quartic curves. (English) Zbl 0983.11067 J. Algebra 226, No. 1, 283-294 (2000). Reviewer: Jannis A.Antoniadis (Iraklion) MSC: 11R58 14H05 PDFBibTeX XMLCite \textit{K. Miura} and \textit{H. Yoshihara}, J. Algebra 226, No. 1, 283--294 (2000; Zbl 0983.11067) Full Text: DOI
Byeon, Dongho Class number 3 problem for the simplest cubic fields. (English) Zbl 0981.11034 Proc. Am. Math. Soc. 128, No. 5, 1319-1323 (2000). Reviewer: Franz Lemmermeyer (Bonn) MSC: 11R16 11R29 PDFBibTeX XMLCite \textit{D. Byeon}, Proc. Am. Math. Soc. 128, No. 5, 1319--1323 (2000; Zbl 0981.11034) Full Text: DOI
Grundman, H. G. Explicit resolutions of cubic cusp singularities. (English) Zbl 0999.11023 Math. Comput. 69, No. 230, 815-825 (2000). MSC: 11F41 11Y40 14E15 14G35 11R16 11R42 PDFBibTeX XMLCite \textit{H. G. Grundman}, Math. Comput. 69, No. 230, 815--825 (2000; Zbl 0999.11023) Full Text: DOI