The Feynman path integral in p-adic quantum mechanics is considered. The probability amplitude K p (x ′′ , t ′′ ; x ′ , t ′) for one-dimensional systems with quadratic actions is calculated in an exact form, which is the same as that in ordinary quantum mechanics.

Abstract This research investigates the boundedness of a p -adic fractional integral operator on Morrey–Herz spaces. In particular, central bounded mean oscillations $(C\dot{M}O)$ (CM?O) and Lipschitz est...

The purpose of this paper is to derive some identities of the higher order generalized twisted Bernoulli numbers and polynomials attached to χ from the properties of the p-adic invariant integral. We give some interesting identities for the power sums and the generalized twisted Bernoulli numbers and polynomials of higher order using the symmetric properties of the p-adic invariant integral. 20...

In this short survey we look at a few basic features of p-adic numbers, somewhat with the point of view of a classical analyst. In particular, with p-adic numbers one has arithmetic operations and a norm, just as for real or complex numbers. Let Z denote the integers, Q denote the rational numbers, R denote the real numbers, and C denote the complex numbers. Also let | · | denote the usual abso...

In this paper, we construct Chern class maps and cycle class maps with values in p-adic étale Tate twists [Sa2]. We also relate the p-adic étale Tate twists with the finite part of Bloch-Kato. As an application, we prove that the integral part of p-adic regulator maps has values in the finite part of Galois cohomology under certain assumptions. 2000 Mathematics Subject Classification: Primary 1...

In this short survey we look at a few basic features of p-adic numbers, somewhat with the point of view of a classical analyst. In particular, with p-adic numbers one has arithmetic operations and a norm, just as for real or complex numbers. Let Z denote the integers, Q denote the rational numbers, R denote the real numbers, and C denote the complex numbers. Also let | · | denote the usual abso...

In 2008, Jang et al. constructed generating functions of the multiple twisted Carlitz’s type qBernoulli polynomials and obtained the distribution relation for them. They also raised the following problem: “are there analytic multiple twisted Carlitz’s type q-zeta functions which interpolate multiple twisted Carlitz’s type q-Euler (Bernoulli) polynomials?” The aim of this paper is to give a part...

Let E be an elliptic curve which is defined over Q and has stable reduction modulo a given prime p. Assuming that E is modular, one can associate to E a p-adic L-function Lp(E, s). (See [-Mz-SwD, A-V, Vi, Mz-T-T] for its construction in various cases.) This function is defined by a certain interpolation property and is analytic for seZp. In this paper, we will assume that E has split multiplica...

We study the p-adic behavior of Jacobi sums for Q(ζp) and link this study to the p-Sylow subgroup of the class group of Q(ζp) + and to some properties of the jacobian of the Fermat curve Xp + Y p = 1 over Fl where l is a prime number distinct from p. Let p be a prime number, p ≥ 5. Iwasawa has shown that the p-adic properties of Jacobi sums for Q(ζp) are linked to Vandiver’s Conjecture (see [5]...