Theoretical analysis reveals partial q-analogues for Swisher conjectures (A.3) and (D.3), confirming weakened supercongruence identities proposed by Guo, Zudilin, Liu, and Wang.
In this paper, by making use of the creative microscoping method introduced by Guo and Zudilin [Adv. Math. 346 (2019), 329-358] and the Chinese remainder theorem for coprime polynomials, we establish partial q-analogues of Swisher’s conjectures (A.3) and (D.3), thereby partially confirming them. In particular, we respectively obtain weakened forms of the conjectures proposed by Guo and Zudilin, and by Liu and Wang.
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Li et al. (2026) studied this question.
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