»ã±¨±êÌâ (Title)£º¡°·¢É¢¡±RamanujanÐͳ¬Í¬ÓàµÄÒ»¸öеÄq-·ÂÕÕ£¨A new q-analogue of a ``divergent" Ramanujan-type supercongruence£©

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»ã±¨¹¦·ò (Time)£º2023Äê11ÔÂ1ÈÕ(ÖÜÈý) 15:00¡ª16:00

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»ã±¨ÌáÒª£ºGuillera and Zudilin proved the following ``divergent" Ramanujan- type supercongruence: for any odd prime p, \sum_{k=0}^{p-1} \frac{(\frac{1}{2})_k^3}{k!^3}(3k+1)2^{2k} \equiv p\pmod{p^3}. Sun further conjectured that the above supercongruence is also true modulo p^4 for p>3, and a q-analogue of this result was given by the author in an early paper. In this paper, we establish a new q-analogue of Sun's supercongruence by employing the method of ``creative microscoping", developed by the author and Zudilin in 2019.