Related papers: On Some p-Adic Series with Factorials

$p$-adic continued fractions, as an extension of the classical concept of classical continued fractions to the realm of $p$-adic numbers, offering a novel perspective on number representation and approximation. While numerous $p$-adic…

For a prime $p$ and an integer $x$, the $p$-adic valuation of $x$ is denoted by $\nu_{p}(x)$. For a polynomial $Q$ with integer coefficients, the sequence of valuations $\nu_{p}(Q(n))$ is shown to be either periodic or unbounded. The first…

The factorial moments of the standard Poisson distribution are well known. The present note presents an explicit combinatorial sum for the factorial moments of the Poisson distribution of order $k$. Unlike the standard Poisson distribution…

We extend previous work of the author using an idea of Buzzard and give an elementary construction of non-ordinary $p$-adic families of Hilbert Modular Eigenforms.

it is the purpose of this paper to construct a p-adic continuous function for an odd prime to contain a p-adic q-analogue of higher order Dedekind type sums related to q-Euler polynomials and numbers.

In the recent p-adic q-integral on the p-adic integers' rings was constructed >. The purpose of this paper is to give several interesting integral equation for the p-adic q-integerals on the rings of p-adic integers. As an integral…

In this paper, we will constructed p-adic twisted q-l-functions which is a part of answer of the question in [8]. Finally, we will treat many interesting properties related to twisted q-Euler numbers and polynomials.

A difference equation based method of determining two factors of a composite is presented. The feasibility of P-complexity is shown. Presentation of material is non-theoretical; intended to be accessible to a broader audience of non…

We show that the compositions of positive integers may be interpreted in terms of powers of some power series, over arbitrary commutative ring. As consequences, several closed formulas for the compositions as well as for the generalized…

This survey describes work on the number of variables required to ensure that a system of r quadratic forms over the p-adics has a non-trivial common zero.

We examine the behavior of the sequences of $p$-adic valuations of quadratic polynomials with integer coefficients for an odd prime $p$ through tree representations. Under this representation, a finite tree corresponds to a periodic…

We classify the filtered modules with coefficients corresponding to two-dimensional potentially semi-stable $p$-adic representations of the absolute Galois groups of $p$-adic fields under the assumptions that $p$ is odd and the coefficients…

A complete list of one dimensional groups definable in the p-adic numbers is given, up to a finite index subroup and a quotient by a finite subgroup.

We prove that $p$-determinants of a certain class of differential operators can be lifted to power series over $\mathbb{Q}$. We compute these power series in terms of monodromy of the corresponding differential operators.

In this paper, we study properties of polynomials over division rings. Moreover, we present formulas for finding roots of some polynomials

We study the roots of a random polynomial over the field of p-adic numbers. For a random monic polynomial with coefficients in $\mathbb{Z}_p$, we obtain an asymptotic formula for the factorial moments of the number of roots of this…

We prove in particular that, in a large class of dp-minimal theories including the p-adics, definable types are dense amongst non-forking types.

We study finite groups which possess a strongly p-embedded subgroup for some odd prime p. The main results of the paper will be applied in the ongoing project to classify the simple groups of local characteristic p.

We attempt to quantify the exact proportion of monic $p$-adic polynomials of degree $n$ which are irreducible. We find an exact answer to this when $n$ is prime and $p \neq n$, and also when $n = 4$ and $p \neq 2$. Our answers are rational…

In this paper, a randomized algorithm for deciding the irreducibility of an irreducible polynomial and factoring a reducible polynomial over the field of rational numbers is presented. The main idea underlying the algorithm is based on…