SPECIAL VALUES OF HYPERGEOMETRIC FUNCTIONS AND PERIODS OF CM ELLIPTIC CURVES

被引：1

作者：

Yang, Yifan ^{[1
,2
]}

机构：

[1] Natl Taiwan Univ, Dept Math, Taipei 106, Taiwan

[2] Natl Ctr Theoret Sci, Taipei 106, Taiwan

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 370卷 / 09期

关键词：

DIFFERENTIAL-EQUATIONS; AUTOMORPHIC-FORMS; EISENSTEIN SERIES; INTEGRALS;

D O I：

10.1090/tran/7134

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X-0(6)(1)/W-6 be the Atkin-Lehner quotient of the Shimura curve X-0(6)(1) associated to a maximal order in an indefinite quaternion algebra of discriminant 6 over Q. By realizing modular forms on X-0(6)(1)/W6 in two ways, one in terms of hypergeometric functions and the other in terms of Borcherds forms, and using Schofer's formula for values of Borcherds forms at CM-points, we obtain special values of certain hypergeometric functions in terms of periods of elliptic curves over (Q) over bar with complex multiplication.

引用

页码：6433 / 6467

页数：35

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