2013/01/15 by Yifan Yang, Yang, Yifan
Mathematics · #11F12 #11Y60 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F12 #msc:11Y60
paper · pdf · doi:10.48550/arxiv.1301.3344
23 pages
openalex publication_date 2013/01/15 · arxiv created 2013/03/25 · arxiv updated 2013/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1914, Ramanujan gave a list of 17 identities expressing 1/π 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 products of Gamma values. The product of Gamma values are related to periods of elliptic curves with complex multiplication by Q(√(-3)) and Q(√(-4)).