Abstract
Kampé de Fériet hypergeometric functions are two-variable hypergeometric functions, which are a generalization of Appell’s functions. It is known that they satisfy many reduction and summation formulas. In this paper, we define Kampé de Fériet hypergeometric functions over finite fields and show analogous formulas.
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Acknowledgements
The authors would like to thank Noriyuki Otsubo and Takato Senoue for valuable discussions. They also would like to thank Shinichi Kobayashi and Noriyuki Otsubo for a lot of helpful comments on a draft version of this paper. Finally, they would like to thank the anonymous referees for many helpful comments and suggestions. The second author was supported by JSPS KAKENHI Grant Number JP22J21285 and WISE program (MEXT) at Kyushu University. The third author was supported by JST SPRING, Grant Number JPMJSP2109. The fourth author was supported by Waseda University Grant for Special Research Projects, Project Number 2022C-294.
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Ito, R., Kumabe, S., Nakagawa, A. et al. Kampé de Fériet hypergeometric functions over finite fields. Res. number theory 9, 52 (2023). https://doi.org/10.1007/s40993-023-00460-y
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DOI: https://doi.org/10.1007/s40993-023-00460-y