Title

p-adic analogues of Ramanujan type formulas for 1/π

Document Type

Article

Publication Date

3-1-2013

Abstract

Following Ramanujan's work on modular equations and approximations of π, there are formulas for 1/π of the form for d = 2, 3, 4, 6, where λd are singular values that correspond to elliptic curves with complex multiplication, and α, δ are explicit algebraic numbers. In this paper we prove a p-adic version of this formula in terms of the so-called Ramanujan type congruence. In addition, we obtain a new supercongruence result for elliptic curves with complex multiplication.

Publication Source (Journal or Book title)

Mathematics

First Page

9

Last Page

30

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