Divergent Ramanujan-type supercongruences

By Jesús Guillera, Wadim Zudilin. 2010

73 citations recorded by the source corpus.

"Divergent" Ramanujan-type series for $1/\pi$ and $1/\pi^2$ provide us with new nice examples of supercongruences of the same kind as those related to the convergent cases. In this paper we manage to prove three of the supercongruences by means of the Wilf--Zeilberger algorithmic technique.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/4b3efdb301d9792c570316efe630fb6e2f3053ca

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In Algebra and Number Theory

1. Victor J. W. Guo
2. Wadim Zudilin
3. Ji-Cai Liu
4. Su-Dan Wang
5. Holly Swisher
6. Zhi-Wei Sun
7. Armin Straub
8. Michael J. Schlosser

In Applied Mathematics

1. Victor J. W. Guo
2. Wadim Zudilin

Citations in the corpus

• On sums involving products of three binomial coefficients (2010, unknown): “ 2k k 3 ≡ p −1 p +p3E p−3 (mod p 4) provided p > 3, where E0,E1,E2,... are Euler numbers given by E0 = 1 and Xn k=0 2|k n k En−k = 0 (n = 1,2,3,...). The last congruence is still open but [GZ] confirmed that pX−1 k=0 3k +1 (−8)k 2k k 3 ≡ p −1 p (mod p3). SUMS INVOLVING PRODUCTS OF BINOMIAL ”
• A q-microscope for supercongruences (2018, background): “The first author obtained in [12] the following qanalogues of two ‘divergent’ Ramanujan-type supercongruences of Guillera and the second author [7]: m ∑”