On Some Conjectures Related to a Quadratic Transformation of Rahman

Abstract

Through the Chinese remainder theorem for coprime polynomials and the ‘creative microscoping’ method, we establish several new parametric q-supercongruences modulo the fourth powers of a cyclotomic polynomial, whose corresponding congruences can be regarded as variations of Van Hamme’s (J.2) supercongruence. Meanwhile, we confirm some supercongruence conjectures of Tang, Guo and He.

Keywords

q-supercongruence / supercongruence / creative microscoping / cyclotomic polynomial / 33D15 / 11A07 / 11B65

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Peking University