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arXiv · 1904.00490

Some new $q$-congruences for truncated basic hypergeometric series: even powers

Victor J. W. Guo·Michael J. Schlosser
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Abstract

We provide several new $q$-congruences for truncated basic hypergeometric series with the base being an even power of $q$. Our results mainly concern congruences modulo the square or the cube of a cyclotomic polynomial and complement corresponding ones of an earlier paper containing $q$-congruences for truncated basic hypergeometric series with the base being an odd power of $q$. We also give a number of related conjectures including $q$-congruences modulo the fifth power of a cyclotomic polynomial and a congruence for a truncated ordinary hypergeometric series modulo the seventh power of a prime greater than 3.

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Victor J. W. Guo, Michael J. Schlosser. 2019-03-31. Some new $q$-congruences for truncated basic hypergeometric series: even powers. https://doi.org/10.1007/s00025-019-1126-4

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