Academic Journal
p−Adic Analogues of Ramanujan Type Formulas for 1/π
| العنوان: | p−Adic Analogues of Ramanujan Type Formulas for 1/π |
|---|---|
| المؤلفون: | Sarah Chisholm, Alyson Deines, Ling Long, Gabriele Nebe, Holly Swisher |
| المساهمون: | The Pennsylvania State University CiteSeerX Archives |
| المصدر: | http://www.mdpi.com/2227-7390/1/1/9/pdf?y=1. |
| سنة النشر: | 2013 |
| المجموعة: | CiteSeerX |
| مصطلحات موضوعية: | hypergeometric series |
| الوصف: | Following Ramanujan’s work on modular equations and approximations of π, there are formulas for 1/π of the form k=0 ( 1 2 1 d−1)k ()k( d d)k k! 3 (ak + 1)(λd) k = δ π for d = 2, 3, 4, 6, where λd are singular values that correspond to elliptic curves with complex multiplication, and a, 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. |
| نوع الوثيقة: | text |
| اللغة: | English |
| Relation: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.361.3525; http://www.mdpi.com/2227-7390/1/1/9/pdf?y=1 |
| الاتاحة: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.361.3525 http://www.mdpi.com/2227-7390/1/1/9/pdf?y=1 |
| Rights: | Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
| رقم الانضمام: | edsbas.DF65F292 |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |