ρ — Adic Analogues of Ramanujan Type Formulas for 1/π

ρ — Adic Analogues of Ramanujan Type Formulas for 1/π

Following Ramanujan’s work on modular equations and approximations of π, there are formulas for 1/π of the form [PLEASE CHECK FORMULA IN THE PDF] 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....

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Bibliographic Details
Main Authors: Sarah Chisholm, Alyson Deines, Ling Long, Gabriele Nebe, Holly Swisher
Format: Article
Language:English
Published: MDPI AG 2013-03-01
Series:Mathematics
Subjects:
Ramanujan type supercongruences
Atkin and Swinnerton-Dyer congruences
hypergeometric series
elliptic curves
complex multiplication
periods
modular forms
Picard–Fuchs equation
Online Access:http://www.mdpi.com/2227-7390/1/1/9

Internet

http://www.mdpi.com/2227-7390/1/1/9

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