• Corpus ID: 119609827

# New p-adic hypergeometric functions concerning with syntomic regulators

@article{Asakura2018NewPH,
title={New p-adic hypergeometric functions concerning with syntomic regulators},
author={Masanori Asakura},
journal={arXiv: Algebraic Geometry},
year={2018}
}
• M. Asakura
• Published 9 November 2018
• Mathematics
• arXiv: Algebraic Geometry
We introduce new functions, which we call the p-adic hypergeometric functions of logarithmic type. We show the congruence relations that are similar to Dwork's. This implies that they are convergent functions, so that the special values at t=a with |a|=1 are defined under a mild condition. We then show that the special values appear in the syntomic regulators for hypergeometric curves. We expect that they agree with the special values of p-adic L-functions of elliptic curves in some cases.
1 Citations
Congruence relations for p-adic hypergeometric functions $$\widehat{{\mathscr {F}}}_{a,...,a}^{(\sigma )}(t)$$ and its transformation formula
We introduce new kind of $p$-adic hypergeometric functions. We show these functions satisfy congruence relations, so they are convergent functions. And we show that there is a transformation formula

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