$$p$$-Adic Incomplete Gamma Functions and Artin-Hasse-Type Series

On p-adic Artin L-functions II

Let p be a prime. Iwasawa’s famous conjecture relating Kubota-Leopoldt p-adic L-functions to the structure of certain Galois groups has been proven by Mazur and Wiles in [10]. Wiles later proved a far-reaching generalization involving p-adic L-functions for Hecke characters of finite order for a totally real number field in [14]. As we discussed in [5], an analogue of Iwasawa’s conjecture for p...

On the Artin-hasse Exponential Series

1. Professor G. Whaples has kindly drawn my attention to the very similar properties enjoyed by the series which I called the Witt hyperexponential in a recent paper [2], and a series which he had previously defined, using the Artin-Hasse exponential series [5]; the main fact is that both series define a homomorphism of the Witt group W onto the multiplicative group W*. In answer to his questio...

On p-adic multiple zeta and log gamma functions

We define p-adic multiple zeta and log gamma functions using multiple Volkenborn integrals, and develop some of their properties. Although our functions are close analogues of classical Barnes multiple zeta and log gamma functions and have many properties similar to them, we find that our p-adic analogues also satisfy reflection functional equations which have no analogues to the complex case. ...

p-ADIC PERIODS, p-ADIC L-FUNCTIONS, AND THE p-ADIC UNIFORMIZATION OF SHIMURA CURVES

ON p-ADIC POWER SERIES

We obtained the region of convergence and the summation formula for some modified generalized hypergeometric series (1.2). We also investigated rationality of the sums of the power series (1.3). As a result the series (1.4) cannot be the same rational number in all Zp. 1991 Mathematics Subject Classification: 40A30,40D99