On the (K.2) supercongruence of Van Hamme

By Robert Osburn, Wadim Zudilin. 2015

63 citations recorded by the source corpus.

Abstract We prove the last remaining case of the original 13 Ramanujan-type supercongruence conjectures due to Van Hamme from 1997. The proof utilizes classical congruences and a WZ pair due to Guillera. Additionally, we mention some future directions concerning this type of supercongruence.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/9c6c8e912ff436bcfb2b0b5c9387f409004151cb

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

Citations in the corpus

On the supercongruence conjectures of van Hamme (2015, methodology): “2) has been recently proven by Osburn and Zudilin using the W-Z method [16].”
A family of q-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial (2019, background): “It should be pointed out that all of the 13 supercongruences have been proved by different techniques (see [27,31]).”
On Van Hamme's (A.2) and (H.2) supercongruences (2018, methodology): “We refer to [8, 12] for more recent developments on van Hamme’s supercongruences.”
Hypergeometric Functions over Finite Fields (2015, methodology): “See [20] for a general result, and [63] by the second and third authors, [85] by the fourth author, [71] by Osburn and Zudilin for some recent developments on Ramanujan-type supercongruences.”
A q-microscope for supercongruences (2018, methodology): “Development of methods [7, 20–22, 24, 25, 27, 31, 32, 34] for establishing Ramanujan-type supercongruences like (2) and (3), sometimes modulo a smaller power of p and normally on a case-by-case study, was mainly hypergeometric.”
q-Analogues of two Ramanujan-type formulas for 1/π (2018, background): “All the 13 Ramanujan-type supercongruences have now been confirmed by different authors (see [6]).”