Let p be a fixed odd prime number. Throughout this paper Zp,Qp, and Cp will denote the ring of p-adic rational integers, the field of p-adic rational numbers, and the completion of the algebraic closure of Qp. Let N be the set of natural numbers and Z N ∪ {0}. The p-adic norm on Cp is normalized so that |p|p p−1. Let C Zp be the space of continuous functions on Zp. For f ∈ C Zp , the fermionic ...

In his famous Bourbaki talk [2], Deligne described a recipe for attaching `-adic Galois representations to elliptic modular forms of integral weight at least 2. As a consequence of the method, one reduces the Ramanujan–Petersson conjecture to the validity of Weil’s Riemann Hypothesis for varieties over finite fields. There seems to exist no brief and precise outline of Deligne’s recipe in circu...

We are interested in understanding and describing the p-adic properties of Jacobi forms. As opposed to the case of modular forms, not much work has been done in this area. The literature includes [3, 4, 7]. In the first section, we follow Serre’s ideas from his theory of p-adic modular forms. We study Jacobi forms whose Fourier expansions have integral coefficients and look at congruences betwe...

Herrlich showed that a Mumford curve of genus g > 1 over the p-adic complex field Cp has at most 48(g− 1), 24(g− 1), 30(g− 1) or 12(g− 1) automorphisms as p = 2, 3, 5 or p > 5. The Mumford curves attaining these bounds are uniformised by normal subgroups of finite index in certain p-adic triangle groups ∆p for p ≤ 5, or in a p-adic quadrangle group p for p > 5. The finite groups attaining these...

Let p be a fixed odd prime number. Throughout this paper, Zp, Qp, and Cp will denote the ring of p-adic rational integers, the field of p-adic rational numbers, and the completion of algebraic closure of Qp, respectively. The p-adic norm is normalized so that |p|p 1/p. Let N be the set of natural numbers and Z N ∪ {0}. Let UD Zp be the space of uniformly differentiable functions on Zp. For f ∈ ...

Feedback with Carry Shift Registers (FCSR) were introduced by M. Goresky and A. Klapper in 1993. They are very similar to classical Linear Feedback Shift Registers (LFSR) used in many pseudorandom generators. The main difference is the fact that the elementary additions are not additions modulo 2 but with propagation of carries. In this paper we propose a new generator designed from a FCSR auto...

In this paper, we investigate some properties for the q-tangent numbers and polynomials. By using these properties, we give some interesting identities on the q-tangent polynomials and Bernstein polynomials. Throughout this paper, let p be a fixed odd prime number. The symbol, Zp, Qp and Cp denote the ring of p-adic integers, the field of p-adic rational numbers and the completion of algebraic ...

Recently, Y. He derived several identities of symmetry for Carlitz’s q-Bernoulli numbers and polynomials by working over the complex field and using q-zeta functions and standard techniques. In this paper, we work over the p-adic field and use the p-adic q-integrals on Zp in order to get the results obtained earlier by him. 664 Dae San Kim, Taekyun Kim, Sang-Hun Lee and Jong-Jin Seo

In this paper we study some problems related with the theory of multidimensional p-adic wavelets in connection with the theory of multidimensional p-adic pseudo-differential operators (in the p-adic Lizorkin space). We introduce a new class of n-dimensional p-adic compactly supported wavelets. In one-dimensional case this class includes the Kozyrev p-adic wavelets. These wavelets (and their Fou...

Abstract The Chabauty–Kim method is a tool for finding the integral or rational points on varieties over number fields via certain transcendental p -adic analytic functions arising from Selmer schemes associated to unipotent fundamental group of variety. In this paper we establish several foundational results curves fields. two main ingredients in proof these are an unlikely intersection result...