Acta Mathematica Hungarica最新文献_第2页

On the second irreducibility theorem of I. Schur 论舒尔的第二不可约定理

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2024-11-19 DOI: 10.1007/s10474-024-01478-z

A. Jakhar, R. Kalwaniya

{"title":"On the second irreducibility theorem of I. Schur","authors":"A. Jakhar, R. Kalwaniya","doi":"10.1007/s10474-024-01478-z","DOIUrl":"10.1007/s10474-024-01478-z","url":null,"abstract":"<div>Let (n) be a positive integer different from (8) and (n+1 neq 2^u) for any integer (ugeq 2). Let (phi(x)) belonging to (Z[x]) be a monic polynomial which is irreducible modulo all primes less than or equal to (n+1). Let (a_j(x)) with (0leq jleq n-1) belonging to (Z[x]) be polynomials having degree less than (degphi(x)). Assume that the content of (a_na_0(x)) is not divisible by any prime less than or equal to (n+1). We prove that the polynomial \u0000<div><div>$$\u0000f(x) = a_nfrac{phi(x)^n}{(n+1)!}+ sum _{j=0}^{n-1}a_j(x)frac{phi(x)^{j}}{(j+1)!}\u0000$$</div></div>\u0000is irreducible over the field (Q) of rational numbers. This generalises a well-known result of Schur which states that the polynomial ( sum _{j=0}^{n}a_jfrac{x^{j}}{(j+1)!}) with (a_j in Z) and (|a_0| = |a_n| = 1) is irreducible over (Q). For proving our results, we use the notion of (phi)-Newton polygons and a few results on primes from number theory. We illustrate our result through examples.\u0000</div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"289 - 298"},"PeriodicalIF":0.6,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Geodesic loops on tetrahedra in spaces of constant sectional curvature 等截面曲率空间中四面体上的测地线环

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2024-11-12 DOI: 10.1007/s10474-024-01475-2

A. Borisenko, V. Miquel

{"title":"Geodesic loops on tetrahedra in spaces of constant sectional curvature","authors":"A. Borisenko, V. Miquel","doi":"10.1007/s10474-024-01475-2","DOIUrl":"10.1007/s10474-024-01475-2","url":null,"abstract":"<div>Geodesic loops on tetrahedra were studied only for the Euclidean space and it was known that there are no simple geodesic loops on regular tetrahedra. Here we prove that: 1) In the spherical space, there are no simple geodesic loops on tetrahedra with internal angles (pi/3 < a_i<pi/2)or regular tetrahedra with (a_i=pi/2), and there are three simple geodesic loops for each vertex of a tetrahedra with (a_i > pi/2)and the lengths of the edges (a_i>pi/2). 2) We obtain also a new theorem on simple closed geodesics: If the angles (a_i)of the faces of a tetraedron satisfy (pi/3 < a_i<pi/2)and all faces of the tetrahedron are congruent, then there exist at least (3) simple closed geodesics.\u00003) In the hyperbolic space, for every regular tetrahedron (T)and every pair of coprime numbers ((p,q)), there is one simple geodesic loop of type ((p,q)) through every vertex of (T).\u0000The geodesic loops that we have found on the tetrahedra in the hyperbolic space are also quasi-geodesics.</div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"360 - 375"},"PeriodicalIF":0.6,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-024-01475-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Some properties of the ideal of nowhere dense sets in the common division topology 公除法拓扑中无处稠密集理想的一些性质

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2024-11-11 DOI: 10.1007/s10474-024-01481-4

M. Kwela

引用次数: 0

Concurrent normals problem for convex polytopes and Euclidean distance degree 凸多面体的并发法线问题与欧氏距离度

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2024-11-06 DOI: 10.1007/s10474-024-01483-2

I. Nasonov, G. Panina, D. Siersma

引用次数: 0

Some special Z-symmetric manifolds with applications to space-times and Ricci solitons 一些特殊的z对称流形及其在时空和里奇孤子中的应用

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2024-11-05 DOI: 10.1007/s10474-024-01480-5

B. Kirik Rácz, B. Cindik

引用次数: 0

Discrete reflexivity in topological groups and function spaces 拓扑群与函数空间中的离散自反性

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2024-11-05 DOI: 10.1007/s10474-024-01479-y

V. V. Tkachuk

引用次数: 0

Convolution operators and variable Hardy spaces on the Heisenberg group Heisenberg群上的卷积算子与变Hardy空间

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2024-11-05 DOI: 10.1007/s10474-024-01484-1

P. Rocha

引用次数: 0

Doob's inequality, Burkholder–Gundy inequality and martingale transforms on martingale local Morrey spaces Doob不等式、Burkholder-Gundy不等式和鞅局部Morrey空间上的鞅变换

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2024-11-05 DOI: 10.1007/s10474-024-01485-0

K. -P. Ho

引用次数: 0

On the existence of zero-sum subsequences of distinct lengths over certain groups of rank three 关于某些3阶群上不同长度的零和子序列的存在性

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2024-11-05 DOI: 10.1007/s10474-024-01482-3

X. Li, Q. Y. Yin

引用次数: 0

An algebraic classification of means 手段的代数分类

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2024-10-29 DOI: 10.1007/s10474-024-01471-6

L. R. Berrone

引用次数: 0