期刊
JOURNAL OF COMBINATORIAL THEORY SERIES A
卷 182, 期 -, 页码 -出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcta.2021.105469
关键词
Basic hypergeometric series; Watson's (8)phi(7) transformation; q-Supercongruence
类别
资金
- National Natural Science Foundations of China [12071103, 11661032]
With the help of the creative microscoping method recently introduced by Guo and Zudilin and the Chinese remainder theorem for coprime polynomials, a q-supercongruence with two parameters modulo [n]Phi(n)(q)(3) is established. This confirms a recent conjecture of Guo and gives a complete q-analogue of Long's supercongruence, which is also a generalization of a recent q-supercongruence obtained by Guo and Schlosser.
With the help of the creative microscoping method recently introduced by Guo and Zudilin and the Chinese remainder theorem for coprime polynomials, we establish a q-supercongruence with two parameters modulo [n]Phi(n)(q)(3). Here [n] = (1 - q(n))/(1 - q) and Phi(n)(q) is the n-th cyclotomic polynomial in q. In particular, we confirm a recent conjecture of Guo and give a complete q-analogue of Long's supercongruence. The latter is also a generalization of a recent q-supercongruence obtained by Guo and Schlosser. (C) 2021 Elsevier Inc. All rights reserved.
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