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
收藏
页码：6433 / 6467
页数：35
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