Bergström, Jonas; Howe, Everett W.; Lorenzo García, Elisa; Ritzenthaler, Christophe Lower bounds on the maximal number of rational points on curves over finite fields. (English) Zbl 07783188 Math. Proc. Camb. Philos. Soc. 176, No. 1, 213-238 (2024). MSC: 11G20 14H25 14H30 11R45 PDFBibTeX XMLCite \textit{J. Bergström} et al., Math. Proc. Camb. Philos. Soc. 176, No. 1, 213--238 (2024; Zbl 07783188) Full Text: DOI arXiv OA License
Nguyen, Xuan Tho Rational points on a certain genus 2 curve. (English) Zbl 07738609 C. R., Math., Acad. Sci. Paris 361, 1071-1073 (2023). MSC: 14G05 14H99 11D41 PDFBibTeX XMLCite \textit{X. T. Nguyen}, C. R., Math., Acad. Sci. Paris 361, 1071--1073 (2023; Zbl 07738609) Full Text: DOI
Tho, Nguyen Xuan The equation \(y^2 = x^6+x^2+1\) revisited. (English) Zbl 07726357 Indian J. Pure Appl. Math. 54, No. 3, 760-765 (2023). MSC: 11G05 14G05 PDFBibTeX XMLCite \textit{N. X. Tho}, Indian J. Pure Appl. Math. 54, No. 3, 760--765 (2023; Zbl 07726357) Full Text: DOI
Huang, Tinghao; Lalín, Matilde; Mila, Olivier Spherical Heron triangles and elliptic curves. (English) Zbl 07682960 J. Théor. Nombres Bordx. 35, No. 1, 219-246 (2023). Reviewer: Sungkon Chang (Savannah) MSC: 11G05 14J27 14J28 14H52 11D25 PDFBibTeX XMLCite \textit{T. Huang} et al., J. Théor. Nombres Bordx. 35, No. 1, 219--246 (2023; Zbl 07682960) Full Text: DOI arXiv
Vermeulen, Floris Curves of fixed gonality with many rational points. (English) Zbl 1517.11067 J. Théor. Nombres Bordx. 35, No. 1, 135-149 (2023). MSC: 11G20 14G05 14G15 14M25 PDFBibTeX XMLCite \textit{F. Vermeulen}, J. Théor. Nombres Bordx. 35, No. 1, 135--149 (2023; Zbl 1517.11067) Full Text: DOI arXiv
Hast, Daniel Rayor Explicit two-cover descent for genus 2 curves. (English) Zbl 1506.11095 Res. Number Theory 8, No. 4, Paper No. 67, 18 p. (2022). Reviewer: Jeroen Sijsling (Ulm) MSC: 11G30 14G05 11Y50 PDFBibTeX XMLCite \textit{D. R. Hast}, Res. Number Theory 8, No. 4, Paper No. 67, 18 p. (2022; Zbl 1506.11095) Full Text: DOI arXiv
Bremner, Andrew; Nguyen Xuan Tho On the Diophantine equation \(x^4+y^4=c\). (English) Zbl 1503.11069 Acta Arith. 204, No. 2, 141-150 (2022). Reviewer: Victor Wang (Princeton) MSC: 11D25 11R27 14G05 PDFBibTeX XMLCite \textit{A. Bremner} and \textit{Nguyen Xuan Tho}, Acta Arith. 204, No. 2, 141--150 (2022; Zbl 1503.11069) Full Text: DOI
Faber, Xander; Vermeulen, Floris On abelian covers of the projective line with fixed gonality and many rational points. (English) Zbl 1518.11050 Int. J. Number Theory 18, No. 10, 2211-2216 (2022); erratum ibid. 19, No. 1, 235-236 (2023). Reviewer: Erik Antonio Rojas Mendoza (Rio de Janeiro) MSC: 11G20 14G05 11G45 14H51 PDFBibTeX XMLCite \textit{X. Faber} and \textit{F. Vermeulen}, Int. J. Number Theory 18, No. 10, 2211--2216 (2022; Zbl 1518.11050) Full Text: DOI arXiv
Dokchitser, Tim Models of curves over discrete valuation rings. (English) Zbl 1482.11088 Duke Math. J. 170, No. 11, 2519-2574 (2021). Reviewer: Christophe Ritzenthaler (Rennes) MSC: 11G20 11G10 14D10 14F20 14H45 PDFBibTeX XMLCite \textit{T. Dokchitser}, Duke Math. J. 170, No. 11, 2519--2574 (2021; Zbl 1482.11088) Full Text: DOI arXiv
Poonen, Bjorn A \(p\)-adic approach to rational points on curves. (English) Zbl 1461.11099 Bull. Am. Math. Soc., New Ser. 58, No. 1, 45-56 (2021). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11G30 11G20 14D07 14D10 14G05 14H25 PDFBibTeX XMLCite \textit{B. Poonen}, Bull. Am. Math. Soc., New Ser. 58, No. 1, 45--56 (2021; Zbl 1461.11099) Full Text: DOI arXiv
Bianchi, Francesca Quadratic Chabauty for (bi)elliptic curves and Kim’s conjecture. (English) Zbl 1479.11113 Algebra Number Theory 14, No. 9, 2369-2416 (2020). MSC: 11G50 11Y50 14H52 11D45 PDFBibTeX XMLCite \textit{F. Bianchi}, Algebra Number Theory 14, No. 9, 2369--2416 (2020; Zbl 1479.11113) Full Text: DOI arXiv
Bhargava, Manjul; Klagsbrun, Zev; Oliver, Robert J. Lemke; Shnidman, Ari \(3\)-isogeny Selmer groups and ranks of abelian varieties in quadratic twist families over a number field. (English) Zbl 1442.14084 Duke Math. J. 168, No. 15, 2951-2989 (2019). Reviewer: G. K. Sankaran (Bath) MSC: 14G05 11G10 PDFBibTeX XMLCite \textit{M. Bhargava} et al., Duke Math. J. 168, No. 15, 2951--2989 (2019; Zbl 1442.14084) Full Text: DOI arXiv Euclid
Balakrishnan, Jennifer; Dogra, Netan; Müller, J. Steffen; Tuitman, Jan; Vonk, Jan Explicit Chabauty-Kim for the split Cartan modular curve of level 13. (English) Zbl 1469.14050 Ann. Math. (2) 189, No. 3, 885-944 (2019). Reviewer: Imin Chen (Burnaby) MSC: 14G05 11Y50 11G50 11G18 PDFBibTeX XMLCite \textit{J. Balakrishnan} et al., Ann. Math. (2) 189, No. 3, 885--944 (2019; Zbl 1469.14050) Full Text: DOI arXiv
Vlăduţ, Serge Lattices with exponentially large kissing numbers. (English) Zbl 1448.11124 Mosc. J. Comb. Number Theory 8, No. 2, 163-177 (2019). Reviewer: Gabriele Nebe (Aachen) MSC: 11H31 11H71 14G15 52C17 PDFBibTeX XMLCite \textit{S. Vlăduţ}, Mosc. J. Comb. Number Theory 8, No. 2, 163--177 (2019; Zbl 1448.11124) Full Text: DOI arXiv Euclid
Balakrishnan, Jennifer S.; Dogra, Netan Quadratic Chabauty and rational points. I: \(p\)-adic heights. (English) Zbl 1401.14123 Duke Math. J. 167, No. 11, 1981-2038 (2018). Reviewer: Michel Waldschmidt (Paris) MSC: 14G05 11G50 14G40 PDFBibTeX XMLCite \textit{J. S. Balakrishnan} and \textit{N. Dogra}, Duke Math. J. 167, No. 11, 1981--2038 (2018; Zbl 1401.14123) Full Text: DOI arXiv
Balakrishnan, Jennifer S.; Besser, Amnon; Müller, J. Steffen Computing integral points on hyperelliptic curves using quadratic Chabauty. (English) Zbl 1376.11053 Math. Comput. 86, No. 305, 1403-1434 (2017). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11G30 11S80 11Y50 14G40 PDFBibTeX XMLCite \textit{J. S. Balakrishnan} et al., Math. Comput. 86, No. 305, 1403--1434 (2017; Zbl 1376.11053) Full Text: DOI arXiv
Erman, Daniel; Wood, Melanie Matchett Semiample Bertini theorems over finite fields. (English) Zbl 1349.14092 Duke Math. J. 164, No. 1, 1-38 (2015). MSC: 14G15 11G25 PDFBibTeX XMLCite \textit{D. Erman} and \textit{M. M. Wood}, Duke Math. J. 164, No. 1, 1--38 (2015; Zbl 1349.14092) Full Text: DOI arXiv Euclid
Flynn, E. V.; Testa, D. Finite Weil restriction of curves. (English) Zbl 1319.11040 Monatsh. Math. 176, No. 2, 197-218 (2015). Reviewer: Szabolcs Tengely (Debrecen) MSC: 11G30 11G10 14H40 PDFBibTeX XMLCite \textit{E. V. Flynn} and \textit{D. Testa}, Monatsh. Math. 176, No. 2, 197--218 (2015; Zbl 1319.11040) Full Text: DOI arXiv
Siksek, Samir; Stoll, Michael The generalised Fermat equation \(x^{2} + y^{3} = z^{15}\). (English) Zbl 1303.11074 Arch. Math. 102, No. 5, 411-421 (2014). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11G30 11G35 14K20 PDFBibTeX XMLCite \textit{S. Siksek} and \textit{M. Stoll}, Arch. Math. 102, No. 5, 411--421 (2014; Zbl 1303.11074) Full Text: DOI arXiv
González-Jiménez, Enrique; Xarles, Xavier On a conjecture of Rudin on squares in arithmetic progressions. (English) Zbl 1314.11059 LMS J. Comput. Math. 17, 58-76 (2014). Reviewer: Sungkon Chang (Savannah) MSC: 11N13 11G30 11B25 11D45 14H25 PDFBibTeX XMLCite \textit{E. González-Jiménez} and \textit{X. Xarles}, LMS J. Comput. Math. 17, 58--76 (2014; Zbl 1314.11059) Full Text: DOI arXiv
Mourao, Michael Extending elliptic curve Chabauty to higher genus curves. (English) Zbl 1377.11078 Manuscr. Math. 143, No. 3-4, 355-377 (2014). MSC: 11G30 11D41 14H25 PDFBibTeX XMLCite \textit{M. Mourao}, Manuscr. Math. 143, No. 3--4, 355--377 (2014; Zbl 1377.11078) Full Text: DOI arXiv
González-Jiménez, Enrique; Xarles, Xavier Five squares in arithmetic progression over quadratic fields. (English) Zbl 1362.11013 Rev. Mat. Iberoam. 29, No. 4, 1211-1238 (2013). MSC: 11B25 11N36 11G30 14H25 PDFBibTeX XMLCite \textit{E. González-Jiménez} and \textit{X. Xarles}, Rev. Mat. Iberoam. 29, No. 4, 1211--1238 (2013; Zbl 1362.11013) Full Text: DOI arXiv
Anbar, Nurdagül; Stichtenoth, Henning Curves of every genus with a prescribed number of rational points. (English) Zbl 1365.11079 Bull. Braz. Math. Soc. (N.S.) 44, No. 2, 173-193 (2013). MSC: 11G20 14G05 14G15 14H05 PDFBibTeX XMLCite \textit{N. Anbar} and \textit{H. Stichtenoth}, Bull. Braz. Math. Soc. (N.S.) 44, No. 2, 173--193 (2013; Zbl 1365.11079) Full Text: DOI
Aubry, Yves; Haloui, Safia; Lachaud, Gilles On the number of points on abelian and Jacobian varieties over finite fields. (Sur le nombre de points rationnels des variétés abéliennes et des jacobiennes sur les corps finis.) (French. English summary) Zbl 1267.14034 C. R., Math., Acad. Sci. Paris 350, No. 19-20, 907-910 (2012). Reviewer: Christophe Ritzenthaler (Marseille) MSC: 14G15 11G10 11G25 PDFBibTeX XMLCite \textit{Y. Aubry} et al., C. R., Math., Acad. Sci. Paris 350, No. 19--20, 907--910 (2012; Zbl 1267.14034) Full Text: DOI arXiv
Stichtenoth, Henning Curves with a prescribed number of rational points. (English) Zbl 1276.11104 Finite Fields Appl. 17, No. 6, 552-559 (2011). Reviewer: Ferruh Özbudak (Ankara) MSC: 11G20 14H25 PDFBibTeX XMLCite \textit{H. Stichtenoth}, Finite Fields Appl. 17, No. 6, 552--559 (2011; Zbl 1276.11104) Full Text: DOI
Beelen, Peter A generalization of Baker’s theorem. (English) Zbl 1219.11174 Finite Fields Appl. 15, No. 5, 558-568 (2009). Reviewer: Kenneth Ward (Stillwater) MSC: 11R58 14H05 PDFBibTeX XMLCite \textit{P. Beelen}, Finite Fields Appl. 15, No. 5, 558--568 (2009; Zbl 1219.11174) Full Text: DOI
Bruin, Nils; Stoll, Michael Two-cover descent on hyperelliptic curves. (English) Zbl 1208.11078 Math. Comput. 78, No. 268, 2347-2370 (2009). Reviewer: Takao Yamazaki (Tohoku) MSC: 11G30 11Y50 14H40 PDFBibTeX XMLCite \textit{N. Bruin} and \textit{M. Stoll}, Math. Comput. 78, No. 268, 2347--2370 (2009; Zbl 1208.11078) Full Text: DOI arXiv
Bogomolov, Fedor; Tschinkel, Yuri Co-fibered products of algebraic curves. (English) Zbl 1186.14029 Cent. Eur. J. Math. 7, No. 3, 382-386 (2009). Reviewer: Scott Corry (Appleton) MSC: 14H30 14L40 14G35 11F06 11E45 11E12 PDFBibTeX XMLCite \textit{F. Bogomolov} and \textit{Y. Tschinkel}, Cent. Eur. J. Math. 7, No. 3, 382--386 (2009; Zbl 1186.14029) Full Text: DOI arXiv
Ghioca, Dragos; Tucker, T. J. Periodic points, linearizing maps, and the dynamical Mordell-Lang problem. (English) Zbl 1186.14047 J. Number Theory 129, No. 6, 1392-1403 (2009). Reviewer: Jorge Pineiro (Bronx) MSC: 14K12 37P35 37P20 14C25 PDFBibTeX XMLCite \textit{D. Ghioca} and \textit{T. J. Tucker}, J. Number Theory 129, No. 6, 1392--1403 (2009; Zbl 1186.14047) Full Text: DOI arXiv
Farashahi, Reza Rezaeian; Pellikaan, Ruud; Sidorenko, Andrey Extractors for binary elliptic curves. (English) Zbl 1182.14033 Des. Codes Cryptography 49, No. 1-3, 171-186 (2008). MSC: 14G50 11T71 14H52 94A60 PDFBibTeX XMLCite \textit{R. R. Farashahi} et al., Des. Codes Cryptography 49, No. 1--3, 171--186 (2008; Zbl 1182.14033) Full Text: DOI
Bruin, N.; Flynn, E. V. Exhibiting SHA[2] on hyperelliptic Jacobians. (English) Zbl 1118.14035 J. Number Theory 118, No. 2, 266-291 (2006). MSC: 14H40 11G30 11G10 14G05 PDFBibTeX XMLCite \textit{N. Bruin} and \textit{E. V. Flynn}, J. Number Theory 118, No. 2, 266--291 (2006; Zbl 1118.14035) Full Text: DOI Link
Girard, Martine; Kulesz, Leopoldo Computation of sets of rational points of genus-3 curves via the Dem’ janenko-Manin method. (English) Zbl 1108.14017 LMS J. Comput. Math. 8, 267-300 (2005). MSC: 14G05 11G30 14Q05 PDFBibTeX XMLCite \textit{M. Girard} and \textit{L. Kulesz}, LMS J. Comput. Math. 8, 267--300 (2005; Zbl 1108.14017) Full Text: DOI Link
Elkies, Noam D.; Howe, Everett W.; Kresch, Andrew; Poonen, Bjorn; Wetherell, Joseph L.; Zieve, Michael E. Curves of every genus with many points. II: Asymptotically good families. (English) Zbl 1072.11041 Duke Math. J. 122, No. 2, 399-422 (2004). Reviewer: Fernando Torres (Campinas) MSC: 11G20 14G05 14G15 PDFBibTeX XMLCite \textit{N. D. Elkies} et al., Duke Math. J. 122, No. 2, 399--422 (2004; Zbl 1072.11041) Full Text: DOI arXiv
Flynn, E. V. The Hasse principle and the Brauer-Manin obstruction for curves. (English) Zbl 1069.11023 Manuscr. Math. 115, No. 4, 437-466 (2004). Reviewer: M. Rafiq Omar (Bellville) MSC: 11G30 11G10 14H40 14H25 14G05 PDFBibTeX XMLCite \textit{E. V. Flynn}, Manuscr. Math. 115, No. 4, 437--466 (2004; Zbl 1069.11023) Full Text: DOI
Schaefer, Edward F.; Stoll, Michael How to do a \(p\)-descent on an elliptic curve. (English) Zbl 1119.11029 Trans. Am. Math. Soc. 356, No. 3, 1209-1231 (2004). MSC: 11G05 14H25 14H52 14K15 PDFBibTeX XMLCite \textit{E. F. Schaefer} and \textit{M. Stoll}, Trans. Am. Math. Soc. 356, No. 3, 1209--1231 (2004; Zbl 1119.11029) Full Text: DOI
Duquesne, Sylvain Rational points and the elliptic Chabauty method. (Points rationnels et méthode de Chabauty elliptique.) (French) Zbl 1097.11014 J. Théor. Nombres Bordx. 15, No. 1, 99-113 (2003). Reviewer: William McCallum (Tucson) MSC: 11D41 11G30 11D45 13J05 14G05 PDFBibTeX XMLCite \textit{S. Duquesne}, J. Théor. Nombres Bordx. 15, No. 1, 99--113 (2003; Zbl 1097.11014) Full Text: DOI Numdam EuDML
Flynn, E. V.; Redmond, J. Application of covering techniques to families of curves. (English) Zbl 1119.14026 J. Number Theory 101, No. 2, 376-397 (2003). MSC: 14H30 11G30 11G10 14H40 14G05 PDFBibTeX XMLCite \textit{E. V. Flynn} and \textit{J. Redmond}, J. Number Theory 101, No. 2, 376--397 (2003; Zbl 1119.14026) Full Text: DOI
Li, Wen-Ching W.; Maharaj, Hiren Coverings of curves with asymptotically many rational points. (English) Zbl 1055.11040 J. Number Theory 96, No. 2, 232-256 (2002). Reviewer: Robert F. Lax (Baton Rouge) MSC: 11G20 14H25 11G09 PDFBibTeX XMLCite \textit{W.-C. W. Li} and \textit{H. Maharaj}, J. Number Theory 96, No. 2, 232--256 (2002; Zbl 1055.11040) Full Text: DOI arXiv
Kresch, Andrew; Wetherell, Joseph L.; Zieve, Michael E. Curves of every genus with many points. I: Abelian and toric families. (English) Zbl 1062.14027 J. Algebra 250, No. 1, 353-370 (2002). MSC: 14G05 11G20 14G15 PDFBibTeX XMLCite \textit{A. Kresch} et al., J. Algebra 250, No. 1, 353--370 (2002; Zbl 1062.14027) Full Text: DOI arXiv