MAHLER MEASURE AND INTEGRALS OF HYPERGEOMETRIC FUNCTIONS

被引:0
作者
Benferhat, Leila [1 ]
机构
[1] USTHB, BP 32 El Alia, Bab Ezzouar, Algeria
来源
JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS | 2008年 / 12卷 / 01期
关键词
Mahler measure; Dirichlet L-series; hypergeometric functions; differential equations;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Boyd studied in [4] the Mahler measure of some families of elliptic curves given by reciprocal polynomials depending on a real parameter l. These curves are of genus 1 except for the singular values of the parameter l and do not vanish on the torus for l large enough. Using the Mahler measure, we prove that the Picard-Fuchs equation associated to one Boyd's family admits explicit solutions at the singularities of the equation and that we can express certain Dirichlet L-series L(chi, 2) as integrals of functions related to the hypergeometric functions F(1/2, 1/2, 1; z).
引用
收藏
页码:49 / 59
页数:11
相关论文
共 5 条
[1]  
Ahlgren S, 2002, INT MATH RES NOTICES, V2002, P1723
[2]  
Berndt BC, 2002, J REINE ANGEW MATH, V551, P33
[3]   An explicit Mahler measure [J].
Bertin, MJ .
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2001, 333 (01) :1-3
[4]   Mahler's measure and special values of L-functions [J].
Boyd, DW .
EXPERIMENTAL MATHEMATICS, 1998, 7 (01) :37-82
[5]  
RODRIGUEZVILLEG.F, 1996, MODULAR MAHLER MEASU