Let p be a fixed prime number. Throughout this paper, the symbols Z, Zp, Qp, and Cp denote the ring of rational integers, the ring of p-adic integers, the field of p-adic rational numbers, and the completion of algebraic closure ofQp, respectively. LetN be the set of natural numbers andZ N∪{0}. Let νp be the normalized exponential valuation ofCp with |p|p p−νp p p−1. Let UD Zp be the space of u...

We compute the integral $p$-adic \'etale cohomology of Drinfeld symmetric spaces any dimension. This refines computation rational from Colmez-Dospinescu-Nizio{\l}. The main tools are: de Rham CDN and comparison theorems Bhatt-Morrow-Scholze \v{C}esnavi\v{c}ius-Koshikawa which replace quasi-integral theorem Tsuji used in CDN.

Let p, q be distinct primes satisfying gcd(p−1, q−1) = d and letDi, i = 0, 1, · · · , d−1, be Whiteman’s generalized cyclotomic classes with Z∗ pq = ∪ d−1 i=0Di. In this paper, we give the values of Gauss periods based on the generalized cyclotomic sets D∗ 0 = ∑ d 2 −1 i=0 D2i and D ∗ 1 = ∑ d 2 −1 i=0 D2i+1. As an application, we determine a lower bound on the 2-adic complexity of modified Jaco...

Let p be a fixed prime number. Throughout this paper, the symbols Z, Zp, Qp, and Cp denote the ring of rational integers, the ring of p-adic integers, the field of p-adic rational numbers, and the completion of algebraic closure of Qp, respectively. Let N be the set of natural numbers. The normalized valuation in Cp is denoted by | · |p with |p|p 1/p. Let UD Zp be the space of uniformly differe...

p-Adic mathematical physics is a branch of modern mathematical physics based on the application of p-adic mathematical methods in modeling physical and related phenomena. It emerged in 1987 as a result of efforts to find a non-Archimedean approach to the spacetime and string dynamics at the Planck scale, but then was extended to many other areas including biology. This paper contains a brief re...

Let Fq be a finite field of cardinality q and characteristic p. Let P (x) be any one-variable Laurent polynomial over Fq of degree (d1, d2) respectively and p d1d2. For any fixed s ≥ 1 coprime to p, we prove that the q-adic Newton polygon of the L-functions of exponential sums of P (xs) has a tight lower bound which we call Hodge-Stickelberger polygon, depending only on the d1, d2, s and the re...

In this paper a countable family of new compactly supported non-Haar p-adic wavelet bases in L(Q p ) is constructed. We use the wavelet bases in the following applications: in the theory of p-adic pseudo-differential operators and equations. Namely, we study the connections between wavelet analysis and spectral analysis of p-adic pseudo-differential operators. A criterion for a multidimensional...