Related papers: Notes on p-adic numbers

This lecture addresses some general ideas behind numerical computations ranging from representation of numbers in computers to stability and accuracy of standard algorithms for some simple mathematical problems.

We describe our online database of finite extensions of the p-adic numbers, and how it can be used to facilitate local analysis of number fields.

In this short note, we give basic enumerative results on colored integer partitions.

These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.

These notes deal with algebras equipped with an involution and related matters.

We calculate extensions between certain irreducible admissible representations of p-adic groups.

This is a survey of some recent developments concerning the p-adic cohomology of algebraic varieties over fields of positive characteristic and local fields of mixed characteristic, plus some related areas like p-adic Hodge theory.

This paper investigates the p-adic valuation trees of degree-2 and degree-3 polynomials in two variables over any prime p, building upon prior research outlined in [14].

In [2], I constructed the p-adic q-integral on Zp. In this paper, we consider the properties of the p-adic invariant p-adic q-integral in the ring of p-adic integers at q=-1. Finally we give the some applications of p-adic q-integration at…

The mathematical basis of p-adic Higgs mechanism discussed in papers [email protected] 9410058-62 is considered in this paper. The basic properties of p-adic numbers, of their algebraic extensions and the so called canonical…

In this note, basing on a certain functional equation of the dilogarithm function, we establish nontrivial lower bounds for the $p$-adic valuation (where $p$ is a given prime number) of some type of rational numbers involving harmonic…

This is a list of questions raised by our joint work arXiv:1412.0737 and its sequels.

We obtain formulas for the coefficients of positive and negative powers of a partial theta function.

Problems in additive number theory related to sum and difference sets, more general binary linear forms, and representation functions of additive bases for the integers and nonnegative integers.

The aim of this note is to provoke discussion concerning arithmetic properties of function $p_{d}(n)$ counting partitions of an positive integer $n$ into $d$-th powers, where $d\geq 2$. Besides results concerning the asymptotic behavior of…

This short note contains elementary evaluations of some Euler sums.

In this paper, we consider degenerate poly-Bernoulli numbers and polynomials associated with polylogarithmic function and p-adic invariant integral on Zp. By using umbral calculus, we derive some identities of those numbers and polynomials

In this paper, we introduce a subclass of p-valent non-bazilavec functions of order. Some subordination relations and the inequality properties of p-valent functions are discussed. The results presented here generalize and improve some…

We design algorithms for computing values of many p-adic elementary and special functions, including logarithms, exponentials, polylogarithms, and hypergeometric functions. All our algorithms feature a quasi-linear complexity with respect…

It is noted that an efficient algorithm for calculating a $p$-adic height could have cryptanalytic applications.