Explicit quadratic Chabauty over number fields

被引:0
|
作者
Jennifer S. Balakrishnan
Amnon Besser
Francesca Bianchi
J. Steffen Müller
机构
[1] Boston University,Department of Mathematics and Statistics
[2] Ben-Gurion University of the Negev,Department of Mathematics
[3] University of Groningen,Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence
来源
关键词
D O I
暂无
中图分类号
学科分类号
摘要
We generalize the explicit quadratic Chabauty techniques for integral points on odd degree hyperelliptic curves and for rational points on genus 2 bielliptic curves to arbitrary number fields using restriction of scalars. This is achieved by combining equations coming from Siksek’s extension of classical Chabauty with equations defined in terms of p-adic heights attached to independent continuous idele class characters. We give several examples to show the practicality of our methods.
引用
收藏
页码:185 / 232
页数:47
相关论文
共 50 条
  • [41] On quaternion algebras that split over specific quadratic number fields
    Acciaro, Vincenzo
    Savin, Diana
    Taous, Mohammed
    Zekhnini, Abdelkader
    Italian Journal of Pure and Applied Mathematics, 2022, 47 : 91 - 107
  • [42] An exact mass formula for quadratic forms over number fields
    Hanke, J
    JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2005, 584 : 1 - 27
  • [43] On quaternion algebras over some extensions of quadratic number fields
    V. Acciaro
    D. Savin
    M. Taous
    A. Zekhnini
    Boletín de la Sociedad Matemática Mexicana, 2021, 27
  • [44] GENERALISED QUADRATIC FORMS OVER TOTALLY REAL NUMBER FIELDS
    Browning, Tim
    Pierce, Lillian B.
    Schindler, Damaris
    JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 2024, 23 (06) : 2859 - 2912
  • [45] The average size of Ramanujan sums over quadratic number fields
    Zhai, Wenguang
    RAMANUJAN JOURNAL, 2021, 56 (03): : 953 - 969
  • [46] The average size of Ramanujan sums over quadratic number fields
    Werner Georg Nowak
    Archiv der Mathematik, 2012, 99 : 433 - 442
  • [47] FINITENESS AND PERIODICITY OF CONTINUED FRACTIONS OVER QUADRATIC NUMBER FIELDS
    Masakova, Zuzana
    Vavra, Tomas
    Veneziano, Francesco
    BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 2022, 150 (01): : 77 - 109
  • [48] The sum of four squares over real quadratic number fields
    Saetan, Uraipan
    Chotigeat, Wilaiwan
    INTERNATIONAL JOURNAL OF NUMBER THEORY, 2024, 20 (01) : 47 - 72
  • [49] New analytic problems over imaginary quadratic number fields
    Motohashi, Y
    NUMBER THEORY, 2001, : 255 - 279
  • [50] THE NUMBER OF STEPS IN THE EUCLIDEAN ALGORITHM OVER COMPLEX QUADRATIC FIELDS
    KNOPFMACHER, A
    KNOPFMACHER, J
    BIT, 1991, 31 (02): : 286 - 292