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Optimal expansions of Kakeya sequences Kakeya 序列的最优展开
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-09-23 DOI: 10.1007/s10474-024-01453-8
A. C. Lai, P. Loreti
{"title":"Optimal expansions of Kakeya sequences","authors":"A. C. Lai,&nbsp;P. Loreti","doi":"10.1007/s10474-024-01453-8","DOIUrl":"10.1007/s10474-024-01453-8","url":null,"abstract":"<div><p>We investigate optimal expansions of Kakeya sequences for the representation of real numbers. Expansions of Kakeya sequences generalize the expansions in non-integer bases and they display analogous redundancy phenomena. In this paper, we characterize optimal expansions of Kakeya sequences, and we provide conditions for the existence of unique expansions with respect to Kakeya sequences.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 1","pages":"1 - 19"},"PeriodicalIF":0.6,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-024-01453-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142672609","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
Average behaviour of Fourier coefficients of (j)-symmetric power (L)-functions over some polynomials 一些多项式上的α-对称幂函数的傅里叶系数的平均行为
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-09-23 DOI: 10.1007/s10474-024-01467-2
A. Sarkar, M. Shahvez Alam
{"title":"Average behaviour of Fourier coefficients of (j)-symmetric power (L)-functions over some polynomials","authors":"A. Sarkar,&nbsp;M. Shahvez Alam","doi":"10.1007/s10474-024-01467-2","DOIUrl":"10.1007/s10474-024-01467-2","url":null,"abstract":"<div><p>We establish the asymptotics of the second moment of the coefficient of <span>(j)</span>-th symmetric poower lift of classical Hecke eigenforms over certain polynomials, given by a sum of triangular numbers with certain positive coefficients. More precisely, for each <span>(j in mathbb{N})</span>, we obtain asymptotics for the sums given by \u0000</p><div><div><span>$$sum_{substack{alpha(underline{x}))+1le X underline{x} in {mathbb Z}^{4}}}\u0000lambda_{ sym^{j}f}^{2}(alpha(underline{x})+1) ,quad sum_{substack{beta(underline{x}))+1le X underline{x} in {mathbb Z}^{4}}}lambda_{ sym^{j}f}^{2}(beta(underline{x})+1)$$</span></div></div><p>,\u0000where <span>(lambda_{ sym^{j}f}^{2}(n))</span> denotes the coefficient of <span>(j)</span>-th symmetric power lift of classical Hecke eigenforms <span>(f)</span>, the polynomials <span>(alpha)</span> and <span>(beta)</span> are given by \u0000</p><div><div><span>$$alpha(underline{x}) = frac{1}{2} big( x_{1}^{2}+ x_{1} + x_{2}^{2} + x_{2} + 2 ( x_{3}^{2} + x_{3}) + 4 (x_{4}^{2} + x_{4}) big) in mathbb {Q}[x_{1},x_{2},x_{3},x_{4}],\u0000$$</span></div></div><p>\u0000and \u0000</p><div><div><span>$$beta(underline{x}) = x_{1}^{2} + frac{x_{2}(x_{2} + 1)}{2} + frac{x_{3}(x_{3}+1)}{2} + 6cdot frac{x_{4}( x_{4}+1)}{2} in {mathbb Q}[x_{1},x_{2},x_{3},x_{4}]$$</span></div></div></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 1","pages":"75 - 93"},"PeriodicalIF":0.6,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142672562","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
Campanato–Morrey spaces and variable Riesz potentials 坎帕纳托-莫雷空间和可变里兹势
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-09-20 DOI: 10.1007/s10474-024-01465-4
T. Ohno, T. Shimomura
{"title":"Campanato–Morrey spaces and variable Riesz potentials","authors":"T. Ohno,&nbsp;T. Shimomura","doi":"10.1007/s10474-024-01465-4","DOIUrl":"10.1007/s10474-024-01465-4","url":null,"abstract":"<div><p>The aim in this note is to show that the variable Riesz potential operator <span>(I_{alpha(cdot)})</span> embeds variable exponent grand Morrey spaces <span>(L^{p(cdot)-0,nu(cdot),theta}(G))</span> into Campanato–Morrey spaces. </p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 1","pages":"62 - 74"},"PeriodicalIF":0.6,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142672709","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
On certain classes of first Baire functionals 关于第一贝叶尔函数的某些类别
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-09-16 DOI: 10.1007/s10474-024-01464-5
J. Mirmina, D. Puglisi
{"title":"On certain classes of first Baire functionals","authors":"J. Mirmina,&nbsp;D. Puglisi","doi":"10.1007/s10474-024-01464-5","DOIUrl":"10.1007/s10474-024-01464-5","url":null,"abstract":"<div><p>We investigate first Baire functionals on the dual ball of a separable Banach space <span>(X)</span> which are pointwise limit of a sequence of <span>(X)</span> whose closed span does not contain any copy of <span>(ell_1)</span> (or has separable dual). We propose an example of a <span>(C(K))</span> space where not all such first Baire functionals exhibit this behavior. \u0000As an application, we study a quantitative version, in terms of descriptive set theory, of family a separable Banach spaces with this peculiarity. </p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 1","pages":"138 - 163"},"PeriodicalIF":0.6,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-024-01464-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249619","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
Groups with some arithmetic conditions on real sub-class sizes 关于实子类大小的一些算术条件的群
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-09-16 DOI: 10.1007/s10474-024-01466-3
G. Qian, Y. Yang
{"title":"Groups with some arithmetic conditions on real sub-class sizes","authors":"G. Qian,&nbsp;Y. Yang","doi":"10.1007/s10474-024-01466-3","DOIUrl":"10.1007/s10474-024-01466-3","url":null,"abstract":"<div><p>We generalize two results about conjugacy class sizes of real elements to sub-class sizes of real elements.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 1","pages":"116 - 120"},"PeriodicalIF":0.6,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249620","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
Covering the permutohedron by affine hyperplanes 用仿射超平面覆盖正多面体
IF 0.9 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-09-13 DOI: 10.1007/s10474-024-01462-7
G. Hegedüs, GY. Károlyi
{"title":"Covering the permutohedron by affine hyperplanes","authors":"G. Hegedüs, GY. Károlyi","doi":"10.1007/s10474-024-01462-7","DOIUrl":"https://doi.org/10.1007/s10474-024-01462-7","url":null,"abstract":"<p>An almost cover of a finite set in the affine space is a collection\u0000of hyperplanes that together cover all points of the set except one. Using the\u0000polynomial method, we determine the minimum size of an almost cover of the\u0000vertex set of the permutohedron and address a few related questions.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"16 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214273","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
Oscillation criterion for generalized Euler difference equations 广义欧拉差分方程的振荡准则
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-09-06 DOI: 10.1007/s10474-024-01460-9
P. Hasil, L. Linhartová, M. Veselý
{"title":"Oscillation criterion for generalized Euler difference equations","authors":"P. Hasil,&nbsp;L. Linhartová,&nbsp;M. Veselý","doi":"10.1007/s10474-024-01460-9","DOIUrl":"10.1007/s10474-024-01460-9","url":null,"abstract":"<div><p>Using a modification of the adapted Riccati transformation, we\u0000prove an oscillation criterion for generalizations of linear and half-linear Euler difference\u0000equations. Our main result complements a large number of previously\u0000known oscillation criteria about several similar generalizations of Euler difference\u0000equations. The major part of this paper is formed by the proof of the main theorem.\u0000To illustrate the fact that the presented criterion is new even for linear\u0000equations with periodic coefficients, we finish this paper with the corresponding\u0000corollary together with concrete examples of simple equations whose oscillatory\u0000properties do not follow from previously known criteria.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 1","pages":"94 - 115"},"PeriodicalIF":0.6,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214274","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
On the structure of the Iwasawa module for (mathbb{Z}_{2})-extensions of certain real biquadratic fields 论某些实双二次域的 $$mathbb{Z}_{2}$ 扩展的岩泽模块结构
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-09-05 DOI: 10.1007/s10474-024-01459-2
A. El Mahi
{"title":"On the structure of the Iwasawa module for (mathbb{Z}_{2})-extensions of certain real biquadratic fields","authors":"A. El Mahi","doi":"10.1007/s10474-024-01459-2","DOIUrl":"10.1007/s10474-024-01459-2","url":null,"abstract":"<div><p>For an infinite family of real biquadratic fields <i>k</i> we give the structure of the Iwasawa module <span>(X=X(k_{infty}))</span> of the <span>(mathbb{Z}_{2})</span>-extension of <i>k</i>. For these fields, we obtain that <span>(lambda=mu=0 mbox{ and }nu=2)</span>. where <span>(lambda)</span>, <span>(mu)</span> and <span>(nu)</span> are the Iwasawa invariants of the cyclotomic <span>(mathbb{Z}_{2})</span>-extension of <i>k</i></p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 1","pages":"49 - 61"},"PeriodicalIF":0.6,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214270","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
The regular topology on C(X, Y) revisited 再论 C（X，Y）上的正则拓扑学
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-09-05 DOI: 10.1007/s10474-024-01463-6
A. Jindal
{"title":"The regular topology on C(X, Y) revisited","authors":"A. Jindal","doi":"10.1007/s10474-024-01463-6","DOIUrl":"10.1007/s10474-024-01463-6","url":null,"abstract":"<div><p>This paper aims to study some important topological properties of the regular topology on <i>C</i>(<i>X</i>, <i>Y</i>), the set of all continuous functions from a Tychonoff space <i>X</i> to a metric space (<i>Y</i>, <i>d</i>). In particular, we study in detail the connectedness of the regular topology on <i>C</i>(<i>X</i>, <i>Y</i>). In the end, some important countability properties are studied.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 1","pages":"234 - 243"},"PeriodicalIF":0.6,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214272","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
On spaces with a (pi)-base whose elements have an H-closed closure 关于元素具有 H 封闭闭合的$$/pi$$-基空间
IF 0.6 3区 数学
Acta Mathematica Hungarica Pub Date : 2024-08-22 DOI: 10.1007/s10474-024-01450-x
D. Giacopello
{"title":"On spaces with a (pi)-base whose elements have an H-closed closure","authors":"D. Giacopello","doi":"10.1007/s10474-024-01450-x","DOIUrl":"10.1007/s10474-024-01450-x","url":null,"abstract":"<div><p>We deal with the class of Hausdorff spaces having a <span>(pi)</span>-base whose elements have an H-closed closure. Carlson proved that <span>(|X|leq 2^{wL(X)psi_c(X)t(X)})</span> for every quasiregular space <span>(X)</span> with a <span>(pi)</span>-base whose elements have an H-closed closure. We provide an example of a space <span>(X)</span> having a <span>(pi)</span>-base whose elements have an H-closed closure which is not quasiregular (neither Urysohn) such that <span>(|X|&gt; 2^{wL(X)chi(X)})</span> (then <span>(|X|&gt; 2^{wL(X)psi_c(X)t(X)})</span>). Always in the class of spaces with a <span>(pi)</span>-base whose elements have an H-closed closure, we establish the bound <span>(|X|leq2^{wL(X)k(X)})</span> for Urysohn spaces and we give an example of an Urysohn space <span>(Z)</span> such that <span>(k(Z)&lt;chi(Z))</span>. Lastly, we present some equivalent conditions to the Martin's Axiom involving spaces with a <span>(pi)</span>-base whose elements have an H-closed closure and, additionally, we prove that if a quasiregular space has a <span>(pi)</span>-base whose elements have an H-closed closure then such a space is Baire.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"173 2","pages":"448 - 460"},"PeriodicalIF":0.6,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142214275","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
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