A further q-analogue of Van Hamme’s (H.2) supercongruence for primes p ≡ 3(mod4)

DOI10.1142/S1793042121500329zbMath1478.33009OpenAlexW3088767759MaRDI QIDQ4995427

Victor J. W. Guo

Publication date: 24 June 2021

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1793042121500329

zbMATH Keywords

basic hypergeometric seriessupercongruences\(q\)-congruencescreative microscoping\(q\)-analogue of Whipple's \(_3 F_2\) sum

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Congruences; primitive roots; residue systems (11A07)

Related Items (15)

A new extension of the (A.2) supercongruence of Van Hamme ⋮ q-Analogues of some supercongruences related to Euler numbers ⋮ Some \(q\)-analogues of supercongruences for truncated \({}_3 F_2\) hypergeometric series ⋮ Some q-supercongruences related to Swisher’s (H.3) conjecture ⋮ Some \(q\)-supercongruences from the Bailey transformation ⋮ \(q\)-supercongruences from squares of basic hypergeometric series ⋮ A new \(q\)-extension of the (H.2) congruence of Van Hamme for primes \(p\equiv 1\pmod{4}\) ⋮ Two \(q\)-congruences involving double basic hypergeometric sums ⋮ Two \(q\)-supercongruences from Watson's transformation ⋮ Factors of certain sums involving central \(q\)-binomial coefficients ⋮ Some \(q\)-supercongruences from a quadratic transformation by Rahman ⋮ \(q\)-supercongruences from transformation formulas ⋮ A \(q\)-supercongruence from a \(q\)-analogue of Whipple's \({}_3F_2\) summation formula ⋮ A -SUPERCONGRUENCE MODULO THE THIRD POWER OF A CYCLOTOMIC POLYNOMIAL ⋮ A new extension of the (H.2) supercongruence of Van Hamme for primes \(p\equiv 3\operatorname{mod}{4}\)

Cites Work

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• Some supercongruences occurring in truncated hypergeometric series
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• Proof of some \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial
• \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial via creative microscoping
• Congruences on sums of \(q\)-binomial coefficients
• On a \(q\)-deformation of modular forms
• Some \(q\)-supercongruences from transformation formulas for basic hypergeometric series
• A q-analogue of the (A.2) supercongruence of Van Hamme for any prime p ≡ 3(mod4)
• Some q-supercongruences for truncated basic hypergeometric series
• Supercongruences for polynomial analogs of the Apéry numbers

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