Proof of Sun’s conjectures on super congruences and the divisibility of certain binomial sums

Mao, Guo-Shuai; Zhang, Tao

doi:10.1007/s11139-019-00138-z

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Cited by 13 publications

(3 citation statements)

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“…which is (1.2) modulo p 3 with r = 1. In 2019, Mao and Zhang [10] confirmed (1.1) via a WZ pair found by Guillera and Zudilin [2]. The reader is referred to [17] for further conjectures involving the sums in (1.1) and (1.2).…”

Section: Introductionmentioning

confidence: 79%

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Proof of some supercongruences concerning truncated hypergeometric series

Wang,

2020

Preprint

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Section: Introductionmentioning

confidence: 79%

“…During the past few decades, supercongruences concerning truncated hypergeometric series have been widely studied (cf. [2,8,10,15,16,20,21,22,23]).…”

Section: Introductionmentioning

confidence: 99%

Proof of some supercongruences concerning truncated hypergeometric series

Wang,

2020

Preprint

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“…In the past decade, many researchers studied supercongruences via the Wilf-Zeilberger (WZ) method (see, for instance, [1,4,6,7,12,14,18,22]). For instance, W. Zudilin [22] proved several Ramanujan-type supercongruences by the WZ method.…”

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confidence: 99%

Proof of two supercongruences by the Wilf-Zeilberger method

Mao

2019

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Some q-Supercongruences from Transformation Formulas for Basic Hypergeometric Series

Guo

Schlosser

2020

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Several new q-supercongruences are obtained using transformation formulas for basic hypergeometric series, together with various techniques such as suitably combining terms, and creative microscoping, a method recently developed by the first author in collaboration with Zudilin. More concretely, the results in this paper include q-analogues of supercongruences (referring to p-adic identities remaining valid for some higher power of p) established by Long, by Long and Ramakrishna, and several other q-supercongruences. The six basic hypergeometric transformation formulas which are made use of are Watson’s transformation, a quadratic transformation of Rahman, a cubic transformation of Gasper and Rahman, a quartic transformation of Gasper and Rahman, a double series transformation of Ismail, Rahman and Suslov, and a new transformation formula for a nonterminating very-well-poised $${}_{12}\phi _{11}$$ 12 ϕ 11 series. Also, the nonterminating q-Dixon summation formula is used. A special case of the new $${}_{12}\phi _{11}$$ 12 ϕ 11 transformation formula is further utilized to obtain a generalization of Rogers’ linearization formula for the continuous q-ultraspherical polynomials.

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Proof of Sun’s conjectures on super congruences and the divisibility of certain binomial sums

Cited by 13 publications

References 8 publications

Proof of some supercongruences concerning truncated hypergeometric series

Proof of some supercongruences concerning truncated hypergeometric series

Proof of two supercongruences by the Wilf-Zeilberger method

Some q-Supercongruences from Transformation Formulas for Basic Hypergeometric Series

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