Related papers: Products of Factorials Modulo p

We review the results having the property of maximal transcendentality.

The sum-product phenomena over a finite extension K of $\mathbb{Q}_p$ is explored. The main feature of the results is the fact that the implied constants are independent of $p$.

We discuss a product formula for $F$-polynomials in cluster algebras, and provide two proofs. One proof is inductive and uses only the mutation rule for $F$-polynomials. The other is based on the Fock-Goncharov decomposition of mutations.…

We study pairs of finitely generated modules over a principal ideal domain and their corresponding matrix representations. We introduce equivalence relations for such pairs and determine invariants and canonical forms.

Let $p$ be an odd prime. For any $p$-adic integer $a$ we let $\overline{a}$ denote the unique integer $x$ with $-p/2<x<p/2$ and $x-a$ divisible by $p$. In this paper we study some permutations involving quadratic residues modulo $p$. For…

We investigate factoriality, Connes' type ${\rm III}$ invariants and fullness of arbitrary amalgamated free product von Neumann algebras using Popa's deformation/rigidity theory. Among other things, we generalize many previous structural…

We survey variety theory for modules of finite dimensional Hopf algebras, recalling some definitions and basic properties of support and rank varieties where they are known. We focus specifically on properties known for classes of examples…

The functional decomposition of polynomials has been a topic of great interest and importance in pure and computer algebra and their applications. The structure of compositions of (suitably normalized) polynomials f=g(h) over finite fields…

We study few properties of square-free integers in certain equations. Using this property, we derive some infinite products in powers of square free numbers. Also, we present a method, to convert power series and trigonometric series to…

Several techniques together with some partial answers are given to the questions of factoriality, type classification and fullness for amalgamated free product von Neumann algebras.

We show that any graph product of residually finite monoids is residually finite. As a special case we obtain that any free product of residually finite monoids is residually finite. The corresponding results for graph products of…

Consider the product of (1-p^(-s))^(-4) over all primes p=1 mod 5. We evaluate its residue at s=1 and compare with the corresponding Mertens constant of Languasco & Zaccagnini. We also count primitive quintic Dirichlet characters mod n and…

We construct polynomial solutions modulo $p^s$ of the differential KZ and dynamical equations where $p$ is an odd prime number.

Let X be a smooth proper curve over a finite field of characteristic p. We prove a product formula for p-adic epsilon factors of arithmetic D-modules on X. In particular we deduce the analogous formula for overconvergent F-isocrystals,…

We study the three term recurrence modulo m. In particular, we prove that Pell numbers modulo m is residue complete if and only m is 2, a power of 3, or a power of 5. Pell-Lucas numbers modulo m is residue complete if and only if m is a…

We completely characterise when the sequence of free subgroup numbers of a finitely generated virtually free group is ultimately periodic modulo a given prime power.

We discuss various factorial properties of subrings as well as properties involving irreducible and square-free elements, in particular ones connected with Jacobian conditions.

In this paper, we study connections between the structure of a group and the structure of the group (under pointwise product) of its polynomial functions.

In this paper, we study the average size of the product of a number and its multiplicative inverse modulo a prime p. This turns out to be related to moments of L-functions and leads to a curious asymptotic formula for a certain triple…

Many generating series of combinatorially interesting numbers have the property that the sum of the terms of order $<p$ at some suitable point is congruent to a zero of a zeta-function modulo infinitely many primes $p$. Surprisingly, very…