Some q-Supercongruences from Singh’s Quadratic Transformation

Abstract

Applying Singh’s quadratic transformation and the “creative microscoping” method (introduced by the author and Zudilin in 2019), the author proves several new q-supercongruences for truncated 4ϕ3 series. Some related conjectures on q-supercongruences are also presented.

Keywords

Cyclotomic polynomials / q-Supercongruences / Singh’s quadratic transformation / Creative microscoping / 33D15 / 11A07 / 11B65

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