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Rouch\'e's Theorem is among the most useful results in complex analysis for counting zeros of analytic functions. Rouch\'e's Theorem also admits a harmonic analogue for counting zeros of complex harmonic functions. Previously, this analogue…

复变函数 · 数学 2026-03-11 Japheth Carlson

For a Lie algebra L over an algebraically closed field of non-zero characteristic, every finite-dimensional L-module can be decomposed into a direct sum of submodules such that all composition factors of a summand have the same character.…

环与代数 · 数学 2013-01-22 Donald W. Barnes

In this paper we prove a finiteness result concerning the Chow group of zero-cycles for varieties over $p$-adic local fields. In this final version, there are several corrections concerning mathematical symbols and reference to related…

代数几何 · 数学 2010-01-24 Shuji Saito , Kanetomo Sato

We show that a sequence over a finite field $\mathbb F_q$ of characteristic $p$ is $p$-automatic if and only if it occurs as a column of the spacetime diagram, with eventually periodic initial conditions, of a linear cellular automaton with…

动力系统 · 数学 2014-12-01 Eric Rowland , Reem Yassawi

In this paper we provide a detailed calculation of the Sweedler cohomology of the algebra of functions on (Z/2)^r, in all degrees, over a field of characteristic 2. The result is strikingly different from the characteristic 0 analog. Then…

量子代数 · 数学 2014-01-21 Pierre Guillot

We study the reverse mathematics of the principle stating that, for every property of finite character, every set has a maximal subset satisfying the property. In the context of set theory, this variant of Tukey's lemma is equivalent to the…

逻辑 · 数学 2012-01-25 Damir D. Dzhafarov , Carl Mummert

We extend a result of Bump et al. to show that a large family of Sheffer sequences has their zeros - up to perhaps a finite number of exceptions - on a vertical line. We connect a particular such sequence to the Riemann zeta function via a…

数论 · 数学 2025-08-26 G. -S. Cheon , T. Forgács , K. Tran

In 1952, Michael posed a question about the functional continuity of commutative Frechet algebras in his memoir, known as Michael problem in the literature. We settle this in the affirmative along with its various equivalent forms, even for…

泛函分析 · 数学 2022-06-29 S. R. Patel

The Lloyd Theorem of (Sol\'e, 1989) is combined with the Schwartz-Zippel Lemma of theoretical computer science to derive non-existence results for perfect codes in the Lee metric, NRT metric, mixed Hamming metric, and for the sum-rank…

组合数学 · 数学 2026-01-21 Minjia Shi , Jing Wang , Patrick Solé

In this paper, we prove some zero density theorems for certain families of Dirichlet $L$-functions. More specifically, the subjects of our interest are the collections of Dirichlet $L$-functions associated with characters to moduli from…

数论 · 数学 2023-09-12 C. C. Corrigan , L. Zhao

We show how finiteness properties of a group and a subgroup transfer to finiteness properties of the Schlichting completion relative to this subgroup. Further, we provide a criterion when the dense embedding of a discrete group into the…

群论 · 数学 2026-01-14 Laura Bonn , Roman Sauer

A rather easy yet rigorous proof of a version of G\"odel's first incompleteness theorem is presented. The version is "each recursively enumerable theory of natural numbers with 0, 1, +, *, =, logical and, logical not, and the universal…

计算机科学中的逻辑 · 计算机科学 2014-05-23 Antti Valmari

We show how to express any Hasse-Schmidt derivation of an algebra in terms of a finite number of them under natural hypothesis. As an application, we obtain coefficient fields of the completion of a regular local ring of positive…

交换代数 · 数学 2007-05-23 M. Fernandez-Lebron , L. Narvaez-Macarro

It is well known that the emptiness problem for binary probabilistic automata and so for quantum automata is undecidable. We present the current status of the emptiness problems for unary probabilistic and quantum automata with connections…

形式语言与自动机理论 · 计算机科学 2016-10-06 Mika Hirvensalo , Abuzer Yakaryılmaz

In this paper we prove a combinatorial theorem for finite labellings of trees, and show that it is equivalent to a theorem for finite covers of metric trees and a fixed point theorem on metric trees. We trace how these connections mimic the…

组合数学 · 数学 2013-07-10 Andrew Niedermaier , Douglas Rizzolo , Francis Edward Su

We prove that $\delta$-derivations of a simple finite-dimensional Lie algebra over a field of characteristic zero, with values in a finite-dimensional module, are either inner derivations, or, in the case of adjoint module, multiplications…

环与代数 · 数学 2022-11-15 Arezoo Zohrabi , Pasha Zusmanovich

A standard graded artinian monomial complete intersection algebra $A=\Bbbk[x_1,x_2,\ldots,x_n]/(x_1^{a_1},x_2^{a_2},\ldots,x_n^{a_n})$, with $\Bbbk$ a field of characteristic zero, has the strong Lefschetz property due to Stanley in 1980.…

交换代数 · 数学 2022-11-28 Ho V. N. Phuong , Quang Hoa Tran

Assuming the generalized Riemann hypothesis, we rediscover and sharpen some of the best known results regarding the distribution of low-lying zeros of Dirichlet $L$-functions. This builds upon earlier work of Omar, which relies on the…

数论 · 数学 2025-03-21 Tianyu Zhao

We study the convergence of a sequence of finite Blaschke products of a fix order toward a rotation. This would enable us to get a better picture of a characterization theorem for finite Blaschke products.

复变函数 · 数学 2014-02-17 Emmanuel Fricain , Javad Mashreghi

A Skolem sequence is a sequence a_1,a_2,...,a_2n (where a_i \in A = {1,...,n }), each a_i occurs exactly twice in the sequence and the two occurrences are exactly a_i positions apart. A set A that can be used to construct Skolem sequences…

组合数学 · 数学 2007-05-23 Gustav Nordh