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 13 条

[1]

Bloch S. J., 2000, CRM Monograph Series, V11

[2]

COATES J, 1987, J REINE ANGEW MATH, V375, P104

[3]

Glasser M. L., 1980, Theoretical Chemistry: Advances and Perspectives, V5, P67

[4]

Goncharov A. B., 1998, LONDON MATH SOC LECT, V254, P147

[5] Zagier's conjecture on L(E,2) [J].

Goncharov, AB ;

Levin, AM .

INVENTIONES MATHEMATICAE, 1998, 132 (02) :393-432

[6]

Koblitz N., 1993, GRADUATE TEXTS MATH, V97

[7]

MESTRE JF, 1991, PROGR MATH, V89, P209

[8]

Ono K., 2004, CBMS REGIONAL C SERI, V102.

[9] The elliptic trilogarithm and Mahler measures of K3 surfaces [J].

Samart, Detchat .

FORUM MATHEMATICUM, 2016, 28 (03) :405-423

[10] Three-variable Mahler measures and special values of modular and Dirichlet L-series [J].

Samart, Detchat .

RAMANUJAN JOURNAL, 2013, 32 (02) :245-268

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