PreprintarXiv licencearXiv
On the syntomic regulator of the Hesse cubic curves and p-adic hypergeometric functions
Abstract
We introduce a new type of p-adic hypergeometric function, which satisfies congruence relations similar to Dwork's p-adic hypergeometric function. Also, we prove that the syntomic regulators of the Hesse cubic curves are expressed in terms of the special values of our new p-adic hypergeometric functions. We also show that there is a transformation formula between our new p-adic hypergeometric function and a p-adic hypergeometric function of logarithmic type defined by Asakura.
Related
- Cubic arithmetic-geometric mean and isogenies of Hesse elliptic curves
- Extensions of several famous combinatorial identities via hypergeometric functions
- Improved criteria for geometric properties of confluent hypergeometric functions
- Exceptional Sets for Certain 2F1 Hypergeometric Functions
- Sharp power-mean comparisons for Gauss hypergeometric functions
BibTeX
@misc{nemoto2026syntomic,
title = {{On the syntomic regulator of the Hesse cubic curves and $p$-adic hypergeometric functions}},
author = {Yusuke Nemoto},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10340},
eprint = {2609.10340},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10340},
}
RIS
TY - UNPB
TI - On the syntomic regulator of the Hesse cubic curves and p-adic hypergeometric functions
AU - Yusuke Nemoto
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.10340
UR - https://arxiv.org/abs/2609.10340
AB - We introduce a new type of p-adic hypergeometric function, which satisfies congruence relations similar to Dwork's p-adic hypergeometric function. Also, we prove that the syntomic regulators of the Hesse cubic curves are expressed in terms of the special values of our new p-adic hypergeometric functions. We also show that there is a transformation formula between our new p-adic hypergeometric function and a p-adic hypergeometric function of logarithmic type defined by Asakura.
ER -