Factors of some truncated basic hypergeometric series

Published 22 Jan 2019 in math.NT and math.CO | (1901.07908v1)

Abstract: We prove that certain basic hypergeometric series truncated at $k=n-1$ have the factor $\Phi_n(q)^2$, where $\Phi_n(q)$ is the $n$-th cyclotomic polynomial. This confirms two recent conjectures of the author and Zudilin. We also put forward some conjectures on $q$-congruences modulo $\Phi_n(q)^2$.

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Authors (1)

Victor J. W. Guo

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