On the Atkin and Swinnerton-Dyer type congruences for some truncated hypergeometric ${}_1F_0$ series

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چکیده

Let $p$ be an odd prime and let $n$ a positive integer with $p\nmid n$. For any $r$ $\lambda \in \{1, 2, 3\}$ \lambda $, we have $$ \sum _{k=0}^{p^{r}n-1}\frac {\left (\frac 12\right )_k}{k!}\cdot \frac {4^k}{\lambda ^

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ژورنال

عنوان ژورنال: Acta Arithmetica

سال: 2021

ISSN: ['0065-1036', '1730-6264']

DOI: https://doi.org/10.4064/aa200405-8-8