Results 91 to 100 of about 25,597,246 (186)

On non-holonomicity, transcendence and $p$-adic valuations

Let $ν_q(n)$ be the p-adic valuation of $n$. We show that the power series with coefficients $ν_q(n)$, respectively $ν_p(n)(\mathrm{ mod\;} k)$, are non-holonomic and not algebraic in characteristic 0. We find infinitely many rational numbers and infinitely many algebraic irrational numbers for which the values of these series are transcendental.
Cobeli, Cristian, Prunescu, Mihai, Zaharescu, Alexandru   +2 more
openaire   +2 more sources

A note on $p$-adic valuations of the Schenker sums

, 2014
A prime number $p$ is called a Schenker prime if there exists such $n\in\mathbb{N}_+$ that $p\nmid n$ and $p\mid a_n$, where $a_n = \sum_{j=0}^{n}\frac{n!}{j!}n^j$ is so-called Schenker sum. T. Amdeberhan, D. Callan and V. Moll formulated two conjectures concerning $p$-adic valuations of $a_n$ in case when $p$ is a Schenker prime.
openaire   +2 more sources

Unlikely intersections on the p-adic formal ball. [PDF]

Res Number Theory, 2023
Serban V.
europepmc   +1 more source

Integer-valued polynomials on valuation rings of global fields with prescribed lengths of factorizations. [PDF]

Mon Hefte Math, 2023
Fadinger-Held V, Frisch S, Windisch D.
europepmc   +1 more source

p-adic vertex operator algebras. [PDF]

Res Number Theory, 2023
Franc C, Mason G.
europepmc   +1 more source

Recovering p$p$‐adic valuations from pro‐p$p$ Galois groups

Journal of the London Mathematical Society
AbstractLet be a field with , where denotes the maximal pro‐2 quotient of the absolute Galois group of a field . We prove that then admits a (non‐trivial) valuation which is 2‐henselian and has residue field . Furthermore, is a minimal positive element in the value group and .
Koenigsmann, J, Strommen, K
openaire   +4 more sources

An Euler system for GU(2, 1). [PDF]

Math Ann, 2022
Loeffler D, Skinner C, Zerbes SL.
europepmc   +1 more source

p-adic Properties of Lengyel's Numbers

, 2014
Lengyel introduced a sequence of numbers Z n , defined combinatorially, that satisfy a recurrence where the coefficients are Stirling numbers of the second kind. He proved some 2-adic properties of these numbers. In this paper, we give another recurrence
D Barsky, Allée Edouard Quincey, J.-P Bézivin   +2 more
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Irreducibility of limits of Galois representations of Saito-Kurokawa type. [PDF]

Res Number Theory, 2021
Berger T, Klosin K.
europepmc   +1 more source

Introduction to p-adic numbers and Hasse-Minkowski theorem

openThe tool of p-adic numbers is of central importance in modern number theory. Given the field Q of rational numbers, one can equip it with the norm induced by the p-adic valuation modulo a prime number p; the field Qp of p-adic numbers modulo p is the
MARINONI, PIETRO
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