Mosaic Supercongruences of Ramanujan Type

Abstract

In this article, we present analogues of supercongruences of Ramanujan type observed by L. Van Hamme and W. Zudilin. Our congruences are inspired by Ramanujan-type series that involve quadratic algebraic numbers.

2000 AMS Subject Classification:

• Primary 11Y55
• 33C20
• Secondary 11B65
• 11D88
• 11F33

Keywords:

• Hypergeometric series
• Supercongruences
• Ramanujan-type series for 1/π and 1/π²
• Ramanujan–Sato-type series

ACKNOWLEDGMENTS

I thank to Wadim Zudilin for encouraging me to discover a pattern in series involving algebraic numbers.