The Iwasawaμ-invariant ofp-adic HeckeL-functions

Integral Properties of Zonal Spherical Functions, Hypergeometric Functions and Invariant

Some integral properties of zonal spherical functions, hypergeometric functions and invariant polynomials are studied for real normed division algebras.

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

A NOTE ON p-ADIC INVARIANT INTEGRAL IN THE RINGS OF p-ADIC INTEGERS

In [2], I constructed the p-adic q-integral I q (f) on Z p. In this paper, we consider the properties of lim q→−1 I q (f) = I −1 (f). Finally we give the some applications of I −1 (f) and integral equations for I −1 (f). These properties are useful and worthwhile to study Euler numbers and polynomials.

T-ADIC L-FUNCTIONS OF p-ADIC EXPONENTIAL SUMS

The T -adic deformation of p-adic exponential sums is defined. It interpolates all classical p-power order exponential sums over a finite field. Its generating L-function is a T -adic entire function. We give a lower bound for its T -adic Newton polygon and show that the lower bound is often sharp. We also study the variation of this L-function in an algebraic family, in particular, the T -adic...

On the /-adic Iwasawa ¿-invariant in a //-extension

For distinct primes / and p , the Iwasawa invariant XT stabilizes in the cyclotomic Zp -tower over a complex abelian base field. We calculate this stable invariant for p = 3 and various / and K. Our motivation was to search for a formula of Riemann-Hurwitz type for XT that might hold in a p-extension. From our numerical results, it is clear that no formula of such a simple kind can hold. In the...