New p-adic hypergeometric functions concerning with syntomic regulators.
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 elliptuic curves in some cases.
Publisher URL: http://arxiv.org/abs/1811.03770