Abstract
In this paper, we give a formula for the number of rational points on the Dwork hypersurfaces of degree six over finite fields by using Greene’s finite-field hypergeometric function, which is a generalization of Goodson’s formula for the Dwork hypersurfaces of degree four. Our formula is also a higher-dimensional and a finite field analogue of Matsumoto-Terasoma-Yamazaki’s formula. Furthermore, we also explain the relation between our formula and Miyatani’s formula.
Acknowledgement
The author is indebted to Professor Shinichi Kobayashi, his supervisor, for his excellent guidance, patience and constant encouragement. He is grateful to Professor Kazuaki Miyatani for informing the author about his result and giving essential advice. He would also like to Professor Noriyuki Otsubo, Akio Nakagawa and Hiroki Obama for valuable comments and discussion.
Citation
Satoshi Kumabe. "Dwork hypersurfaces of degree six and Greene’s hypergeometric function." Hiroshima Math. J. 52 (3) 287 - 310, November 2022. https://doi.org/10.32917/h2020097
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