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- Title
A New q-Variation of the (C.2) Supercongruence of Van Hamme.
- Authors
Guo, Victor J. W.
- Abstract
Long proved that Van Hamme's (C.2) supercongruence is also true modulo p 4 for any prime p > 3 . By making use of the q-WZ method, the author and Wang gave a q-analogue of Long's supercongruence. In this paper, employing the method of 'creative microscoping', introduced by the author and Zudilin in 2019, we obtain a generalization of this q-supercongruence. A limiting case of our result implies that, for 0 ⩽ t ⩽ s ⩽ 10 and any odd prime p ⩾ 4 s + 1 and integer r ⩾ 1 , ∑ k = s (p r - 1) / 2 + s 4 k + 1 256 k 2 k - 2 s k - s 2 k + 2 s k + s 2 k - 2 t k - t 2 k + 2 t k + t ≡ p r (mod p r + 3).
- Subjects
CHINESE remainder theorem
- Publication
Results in Mathematics / Resultate der Mathematik, 2024, Vol 79, Issue 2, p1
- ISSN
1422-6383
- Publication type
Article
- DOI
10.1007/s00025-023-02119-7