Results 51 to 60 of about 13,182 (153)
Relating $p$-adic eigenvalues and the local Smith normal form
, 2015 Conditions are established under which the $p$-adic valuations of the invariant factors (diagonal entries of the Smith form) of an integer matrix are equal to the $p$-adic valuations of the eigenvalues.
Elsheikh, Mustafa, Giesbrecht, Mark
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A classification of Prüfer domains of integer‐valued polynomials on algebras
Bulletin of the London Mathematical Society, Volume 58, Issue 4, April 2026.Abstract Let D$D$ be an integrally closed domain with quotient field K$K$ and A$A$ a torsion‐free D$D$‐algebra that is finitely generated as a D$D$‐module and such that A∩K=D$A\cap K=D$. We give a complete classification of those D$D$ and A$A$ for which the ring IntK(A)={f∈K[X]∣f(A)⊆A}$\textnormal {Int}_K(A)=\lbrace f\in K[X] \mid f(A)\subseteq A ...
Giulio Peruginelli, Nicholas J. Werner
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p-adic valuations of some sums of multinomial coefficients [PDF]
Acta Arithmetica, 2011 Let $m$ and $n>0$ be integers. Suppose that $p$ is a prime dividing $m-4$ but not dividing $m$. We show that $ν_p(\sum_{k=0}^{n-1}\frac{\binom{2k}k}{m^k})$ and $ν_p(\sum_{k=0}^{n-1}\binom{n-1}{k}(-1)^k\frac{\binom{2k}k}{m^k})$ are at least $ν_p(n)$, where $ν_p(x)$ denotes the $p$-adic valuation of $x$. Furthermore, if $p>3$ then $$n^{-1}\sum_{k=0}
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A P‐adic class formula for Anderson t‐modules
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract In 2012, Taelman proved a class formula for L$L$‐series associated to Drinfeld Fq[θ]$\mathbb {F}_q[\theta]$‐modules and considered it as a function field analogue of the Birch and Swinnerton‐Dyer conjecture. Since then, Taelman's class formula has been generalized to the setting of Anderson t$t$‐modules.
Alexis Lucas
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On the P-Adic Valuations of Stirling Numbers of the Second Kind
Contemporary Mathematics, 2021 In this paper, we introduced certain formulas for p-adic valuations of Stirling numbers of the second kind S(n, k) denoted by vp(S(n, k)) for an odd prime p and positive integers k such that n ≥ k. We have obtained the formulas, vp(S(n, n − a)) for a = 1, 2, 3 and vp(S(cpn, cpk )) for 1 ≤ c ≤ p − 1 and primality test of positive integer n.
null S. S. Singh +2 more
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Some bounds related to the 2‐adic Littlewood conjecture
Mathematika, Volume 72, Issue 2, April 2026.Abstract For every irrational real α$\alpha$, let M(α)=supn⩾1an(α)$M(\alpha) = \sup _{n\geqslant 1} a_n(\alpha)$ denote the largest partial quotient in its continued fraction expansion (or ∞$\infty$, if unbounded). The 2‐adic Littlewood conjecture (2LC) can be stated as follows: There exists no irrational α$\alpha$ such that M(2kα)$M(2^k \alpha)$ is ...
Dinis Vitorino, Ingrid Vukusic
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Journal of Approximation Theory, 2003 In this article the authors consider continuous real functions defined on the ring of \(p\)-adic integers \(Z_p\). Given a set \(x_1, x_2, \ldots, x_{p^n}\) of representatives mod \(p^n\), they consider functions of the form \(x \mapsto \lambda_1 |x - x_1|+ \ldots + \lambda_{p^n} |x - x_{p^n}|\).
Khrennikov, Andrei, Radyna, Aliaksandr
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p-Adic valuation of weights in Abelian codes over /spl Zopf/(p/sup d/) [PDF]
, 2005 Counting polynomial techniques introduced by Wilson are used to provide analogs of a theorem of McEliece. McEliece's original theorem relates the greatest power of p dividing the Hamming weights of words in cyclic codes over GF (p) to the length of the ...
Katz, Daniel J.
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Mathematika, Volume 72, Issue 2, April 2026.Abstract In this paper, we study traces of Hecke operators on Drinfeld modular forms of level 1 in the case A=Fq[T]$A = \mathbb {F}_q[T]$. We deduce closed‐form expressions for traces of Hecke operators corresponding to primes of degree at most 2 and provide algorithms for primes of higher degree.
Sjoerd de Vries
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Products of p-Adic Valuation Trees
The PUMP Journal of Undergraduate ResearchThe study of prime divisibility plays a crucial role in number theory. The p-adic valuation of a number is the highest power of a prime, p, that divides that number. Using this valuation, we construct p-adic valuation trees to visually represent the valuations of a sequence.
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