Ramanujan-type identities for Shimura curves

被引：3
作者：
Yang, Yifan [1 ,2 ]
机构：
[1] Natl Chiao Tung Univ, Dept Appl Math, Hsinchu 300, Taiwan
[2] Natl Ctr Theoret Sci, Hsinchu 300, Taiwan
来源：
ISRAEL JOURNAL OF MATHEMATICS | 2016年 / 214卷 / 02期
关键词：
MODULAR-FORMS; SERIES; 1/PI; EQUATIONS; PERIODS;
D O I：
10.1007/s11856-016-1354-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In 1914, Ramanujan gave a list of 17 identities expressing 1/pi as linear combinations of values of hypergeometric functions at certain rational numbers. Since then, identities of similar nature have been discovered by many authors. Nowadays, one of the standard approaches to this kind of identities uses the theory of modular curves. In this paper, we will consider the case of Shimura curves and obtain Ramanujan-type formulas involving special values of hypergeometric functions and periods of elliptic curves over Q with complex multiplication by .
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页码：699 / 731
页数：33
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