Wadim Zudilin - (q-)Supercongruences hit again

hrj:7427 - Hardy-Ramanujan Journal, May 6, 2021, Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2020 - https://doi.org/10.46298/hrj.2021.7427
(q-)Supercongruences hit again

Authors: Wadim Zudilin 1

  • 1 Department of Mathematics and Computer Science, TUE (Eindhoven) and IMAPP, Nijmegen

Using an intrinsic q-hypergeometric strategy, we generalise Dwork-type congruences H(p^{s+1})/H(p^s) ≡ H(p^s)/H(p^{s−1}) (mod p 3) for s = 1, 2,. .. and p a prime, when H(N) are truncated hypergeometric sums corresponding to the periods of rigid Calabi-Yau threefolds.

https://doi.org/10.46298/hrj.2021.7427
Source: HAL:hal-03208276v1
Volume: Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2020
Published on: May 6, 2021
Accepted on: May 6, 2021
Submitted on: April 30, 2021
Keywords: rigid Calabi-Yau threefold,modular form,creative microscoping,q-congruence,supercongruence,Ramanujan's mathematics,Hypergeometric sum,2010 Mathematics Subject Classification. 11A07, 11B65, 11F33, 33C20, 33D15,[MATH]Mathematics [math]

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Source : ScholeXplorer IsRelatedTo HANDLE 2066/214530
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  • 2066/214530
Congruences for q-Binomial Coefficients: To George Andrews, with warm q-wishes and well-looking q-congruences

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