ON A NONCRITICAL SYMMETRIC SQUARE L-VALUE OF THE CONGRUENT NUMBER ELLIPTIC CURVES

被引：0

作者：

Samart, Detchat ^{[1
,2
]}

机构：

[1] Burapha Univ, Dept Math, Chon Buri 20131, Thailand

[2] CHE, Ctr Excellence Math, Bangkok 10400, Thailand

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2020年 / 101卷 / 01期

关键词：

elliptic curve; symmetric square L-function; Eisenstein-Kronecker series; elliptic polylogarithm;

D O I：

10.1017/S000497271900056X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The congruent number elliptic curves are defined by Ed : y2 = x3 d2x, where d 2 N. We give a simple proof of a formula for L(Sym2(Ed); 3) in terms of the determinant of the elliptic trilogarithm evaluated at some degree zero divisors supported on the torsion points on E-d((Q) over bar).

引用

页码：13 / 22

页数：10

共 29 条

[21] Koblitz's conjecture on average for elliptic curves over abelian number fields of square-free conductor
Giberson, Luke
JOURNAL OF NUMBER THEORY, 2018, 185 : 449 - 478
[22] Central value of the symmetric square L-functions related to Hecke–Maass forms
Hengcai Tang
Zhao Xu
Lithuanian Mathematical Journal, 2016, 56 : 251 - 267
[23] Special values of motivic L-functions and zeta-polynomials for symmetric powers of elliptic curves
Steffen Löbrich
Wenjun Ma
Jesse Thorner
Research in the Mathematical Sciences, 4
[24] Special values of motivic L-functions and zeta-polynomials for symmetric powers of elliptic curves
Lobrich, Steffen
Ma, Wenjun
Thorner, Jesse
RESEARCH IN THE MATHEMATICAL SCIENCES, 2017, 4
[25] Central value of the symmetric square L-functions related to Hecke-Maass forms
Tang, Hengcai
Xu, Zhao
LITHUANIAN MATHEMATICAL JOURNAL, 2016, 56 (02) : 251 - 267
[26] Ideal Class Groups of Number Fields and Bloch-Kato?s Tate-Shafarevich Groups for Symmetric Powers of Elliptic Curves
Dainobu, Naoto
TOKYO JOURNAL OF MATHEMATICS, 2022, 45 (02) : 501 - 518
[27] Derivative at s=1 of the p-adic L-function of the symmetric square of an elliptic curve over a totally real field
Rosso, Giovanni
COMPTES RENDUS MATHEMATIQUE, 2013, 351 (7-8) : 251 - 254
[28] The θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\theta }$$\end{document}-Congruent Number Elliptic Curves via Fermat-type Algorithms
Sajad Salami
Arman Shamsi Zargar
Bulletin of the Brazilian Mathematical Society, New Series, 2021, 52 (4) : 893 - 908
[29] Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document} theory for the square roots and square functions of elliptic operators having a BMO anti-symmetric part
Steve Hofmann
Linhan Li
Svitlana Mayboroda
Jill Pipher
Mathematische Zeitschrift, 2022, 301 (1) : 935 - 976

← 1 2 3 →