p-adic integral transforms on compact subgroups of Cp

On p-adic path integral

Feynman's path integral is generalized to quantum mechanics on p-adic space and time. Such p-adic path integral is analytically evaluated for quadratic Lagrangians. Obtained result has the same form as that one in ordinary quantum mechanics. 1. It is well known that dynamical evolution of any one-dimensional quantum-mechanical system, described by a wave function Ψ(x, t), is given by Ψ(x ′′ , t...

INTEGRAL STRUCTURES ON p-ADIC FOURIER THEORY

In this article, we study integral structures on p-adic Fourier theory by Schneider and Teitelbaum. As an application of our result, we give a certain integral basis of the space of K-locally analytic functions for any finite extension K of Qp, generalizing the basis of Amice of locally analytic functions on Zp. We also use our result to prove congruences of Bernoulli-Hurwitz numbers at supersi...

Mellin transforms of p-adic Whittaker functions

Fourier transforms and p - adic Weil

Building on work of Crew, we give a rigid cohomological analogue of the main result of Deligne’s “Weil II”; this makes it possible to give a purely p-adic proof of the Weil conjectures. Ingredients include a p-adic analogue of Laumon’s application of the geometric Fourier transform in the l-adic setting, as well as recent results on p-adic differential equations, due to André, Christol, Crew, M...

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.