The Beilinson conjectures for CM elliptic curves via hypergeometric functions

被引：4
|
作者：
Ito, Ryojun [1 ]
机构：
[1] Chiba Univ, Grad Sch Sci, Dept Math & Informat, Inage Ku, Yayoicho 1-33, Chiba 2638522, Japan
来源：
RAMANUJAN JOURNAL | 2018年 / 45卷 / 02期
关键词：
L-value of elliptic curve; Regulator; Beilinson conjectures; Hypergeometric function; HECKE L-FUNCTIONS; FERMAT-CURVES; VALUES;
D O I：
10.1007/s11139-016-9859-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider certain CM elliptic curves which are related to Fermat curves, and express the values of L-functions at in terms of special values of generalized hypergeometric functions. We compare them and a similar result of Rogers-Zudilin with Otsubo's regulator formulas, and give a new proof of the Beilinson conjectures originally due to Bloch.
引用
收藏
页码：433 / 449
页数：17
相关论文
共 35 条
  • [21] Extended symmetric Pascal matrices via hypergeometric functions
    Cheon, GS
    El-Mikkawy, M
    APPLIED MATHEMATICS AND COMPUTATION, 2004, 158 (01) : 159 - 168
  • [22] On the Lang-Trotter and Sato-Tate Conjectures on Average for Polynomial Families of Elliptic Curves
    Shparlinski, Igor E.
    MICHIGAN MATHEMATICAL JOURNAL, 2013, 62 (03) : 491 - 505
  • [23] Value distribution of twists of L-functions of elliptic curves
    Laurincikas, A.
    Macaitiene, R.
    PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2017, 296 (02) : S70 - S77
  • [24] New subclasses bi-univalent functions related to shell-like curves involving hypergeometric functions
    G. Murugusundaramoorthy
    H. Ö. Güney
    K. Vijaya
    Afrika Matematika, 2020, 31 : 1237 - 1249
  • [25] New subclasses bi-univalent functions related to shell-like curves involving hypergeometric functions
    Murugusundaramoorthy, G.
    Guney, H. O.
    Vijaya, K.
    AFRIKA MATEMATIKA, 2020, 31 (7-8) : 1237 - 1249
  • [26] Elliptic curves, L-functions, and Hilbert's tenth problem
    Murty, M. Ram
    Pasten, Hector
    JOURNAL OF NUMBER THEORY, 2018, 182 : 1 - 18
  • [27] Non-vanishing of central L-values of canonical CM elliptic curves with quadratic twists
    Yao, Cheng
    Hung, Pin-Chi
    MANUSCRIPTA MATHEMATICA, 2016, 150 (3-4) : 293 - 335
  • [28] Vanishing and non-vanishing Dirichlet twists of L-functions of elliptic curves
    Fearnley, Jack
    Kisilevsky, Hershy
    Kuwata, Masato
    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2012, 86 : 539 - 557
  • [29] On the vanishing of twisted L-functions of elliptic curves over rational function fields
    Comeau-Lapointe, Antoine
    David, Chantal
    Lalin, Matilde
    Li, Wanlin
    RESEARCH IN NUMBER THEORY, 2022, 8 (04)
  • [30] Some generating relations for extended hypergeometric functions via generalized fractional derivative operator
    Oezarslan, M. Ali
    Oezergin, Emine
    MATHEMATICAL AND COMPUTER MODELLING, 2010, 52 (9-10) : 1825 - 1833
1234