Results 11 to 20 of about 25,597,246 (186)
p-adic valuation of harmonic sums and their connections with Wolstenholme primes [PDF]
Indian Journal of Pure and Applied Mathematics, 2023 We explore a conjecture posed by Eswarathasan and Levine on the distribution of $p$-adic valuations of harmonic numbers $H(n)=1+1/2+\cdots+1/n$ that states that the set $J_p$ of the positive integers $n$ such that $p$ divides the numerator of $H(n)$ is finite.
Carofiglio L., De Filpo L., Gambini A.
openaire +6 more sources
On the p-adic valuation of harmonic numbers [PDF]
Journal of Number Theory, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sanna, Carlo
openaire +4 more sources
The p-adic valuations of Weil sums of binomials [PDF]
Journal of Number Theory, 2017 26 ...
Langevin, Philippe +3 more
openaire +4 more sources
On p-adic valuations of colored p-ary partitions [PDF]
Monatshefte für Mathematik, 2018 Let $m\in\N_{\geq 2}$ and for given $k\in\N_{+}$ consider the sequence $(A_{m,k}(n))_{n\in\N}$ defined by the power series expansion $$ \prod_{n=0}^{\infty}\frac{1}{\left(1-x^{m^{n}}\right)^{k}}=\sum_{n=0}^{\infty}A_{m,k}(n)x^{n}. $$ The number $A_{m,k}(n)$ counts the number of representations of $n$ as sums of powers of $m$, where each summand has one
Ulas, Maciej, Żmija, Błażej
openaire +3 more sources
One the P-Adic Local Invariant Cycle Theorem [PDF]
, 2012 The aim of this paper is to consider the $p$-adic local invariant cycle theorem in the mixed characteristic case. In the first part of the paper, via case-by-case discussion, we construct the $p$-adic specialization map, and then write out the ...
Wu, Yi-Tao
core +1 more source
Periodicity in the p-adic valuation of a polynomial
Journal of Number Theory, 2017 For a prime $p$ and an integer $x$, the $p$-adic valuation of $x$ is denoted by $ν_{p}(x)$. For a polynomial $Q$ with integer coefficients, the sequence of valuations $ν_{p}(Q(n))$ is shown to be either periodic or unbounded. The first case corresponds to the situation where $Q$ has no roots in the ring of $p$-adic integers.
Medina, Luis A. +2 more
openaire +2 more sources
Representation zeta functions of compact p-adic analytic groups and arithmetic groups [PDF]
, 2013 We introduce new methods from p-adic integration into the study of representation zeta functions associated to compact p-adic analytic groups and arithmetic groups.
Onn, Uri +3 more
core +1 more source
Explicit formulas for the $p$-adic valuations of Fibonomial coefficients II
AIMS Mathematics, 2020 updated and ...
Phakhinkon Phunphayap +1 more
openaire +6 more sources
On the p-adic valuation of stirling numbers of the first kind [PDF]
Acta Mathematica Hungarica, 2016 For all integers $n \geq k \geq 1$, define $H(n,k) := \sum 1 / (i_1 \cdots i_k)$, where the sum is extended over all positive integers $i_1 < \cdots < i_k \leq n$. These quantities are closely related to the Stirling numbers of the first kind by the identity $H(n,k) = s(n + 1, k + 1) / n!$.
LEONETTI, Paolo, SANNA, CARLO
openaire +5 more sources
On p-Adic Estimates of Weights in Abelian Codes over Galois Rings [PDF]
, 2005 Let p be a prime. We prove various analogues and generalizations of McEliece's theorem on the p-divisibility of weights of words in cyclic codes over a finite field of characteristic p. Here we consider Abelian codes over various Galois rings.
Katz, Daniel Jerome
core +1 more source