Acta Mathematica Hungarica最新文献

{"title":"Parallel covering a regular hexagon with squares","authors":"Ziyi Guo,&nbsp;Zhanjun Su","doi":"10.1007/s10474-026-01591-1","DOIUrl":"10.1007/s10474-026-01591-1","url":null,"abstract":"<div><p>Denote by <i>H</i> a regular hexagon with sides of length 1. Let <i>S</i> be a square with a side parallel to a side of <i>H</i> and let <span>({S_{n}})</span> be a collection of the homothetic copies of <i>S</i>. In this note a tight lower bound of the sum of the areas of squares from <span>({S_{n}})</span> that can parallel cover <i>H</i> is determined.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"178 1","pages":"137 - 168"},"PeriodicalIF":0.6,"publicationDate":"2026-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148285384","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}

{"title":"Problems 66 and 67 on sums of residue classes and primes of András Sárközy’s collection of unsolved problems","authors":"Yuchen Ding,&nbsp;Christian Elsholtz,&nbsp;Yu-Chen Sun","doi":"10.1007/s10474-026-01599-7","DOIUrl":"10.1007/s10474-026-01599-7","url":null,"abstract":"<div><p>In this note, we discuss two problems of Sárközy (2001). In particular, we prove an optimal result on sumsets of sparse subset of primes.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"178 1","pages":"130 - 136"},"PeriodicalIF":0.6,"publicationDate":"2026-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-026-01599-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148285381","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}

{"title":"The maximum size of the partial ground set of skew Bollobás systems","authors":"Yu Fang,&nbsp;Tao Feng,&nbsp;Xiaomiao Wang","doi":"10.1007/s10474-026-01594-y","DOIUrl":"10.1007/s10474-026-01594-y","url":null,"abstract":"<div><p>A skew Bollobás system <span>(mathcal {P}={(A_i,B_i):1le ile m})</span> is a collection of pairs of disjoint subsets of [<i>n</i>] such that <span>(A_icap B_jne emptyset )</span> for any <span>(1le i&lt;jle m)</span>. Denote by <span>(S_1(a, b))</span> or <span>(S_2(a, b))</span> the maximum size of <span>(bigcup _{i=1}^m A_i)</span> or <span>(bigcup _{i=1}^m B_i)</span>, respectively, over all possible skew Bollobás systems <span>(mathcal {P}={(A_i,B_i):1le ile m})</span> satisfying <span>(|A_i| le a)</span> and <span>(|B_i| le b)</span> for all <span>(i in [m])</span>. It is shown that for any non-negative integers <i>a</i> and <i>b</i>, <span>(S_1(a,b)=left( {begin{array}{c}a+b+1 aend{array}}right) -1)</span> and <span>(S_2(a,b)=left( {begin{array}{c}a+b+1 a+1end{array}}right) -1)</span>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"178 1","pages":"63 - 67"},"PeriodicalIF":0.6,"publicationDate":"2026-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148285383","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}

{"title":"On density of the zeros of Dedekind zeta-functions","authors":"Wei Zhang","doi":"10.1007/s10474-026-01590-2","DOIUrl":"10.1007/s10474-026-01590-2","url":null,"abstract":"<div><p>For any <span>(sigma )</span> with <span>(0le sigma le 1)</span> and any <span>(T&gt;10)</span> sufficiently large, let <span>(N_{zeta }(sigma ,K,T))</span> be the number of zeros <span>(rho =beta +igamma )</span> of <span>(zeta _{K}(s))</span> with <span>(|gamma |le T)</span> and <span>(beta ge sigma )</span> and the zero being counted according  to multiplicity. For <span>(kge 3)</span>, we have </p><div><div><span>$$ N_{zeta }(sigma ,K,T)ll T^{frac{2k}{6sigma -3}(1-sigma )+varepsilon }, $$</span></div></div><p>where </p><div><div><span>$$ frac{2k+3}{2k+6}le sigma &lt;1 $$</span></div></div><p>and the implied constant may depend on the number field <i>K</i> and <span>(varepsilon )</span>. This improves previous results for <span>(kge 3)</span> of certain range of <span>(sigma )</span>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"178 1","pages":"52 - 62"},"PeriodicalIF":0.6,"publicationDate":"2026-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148285392","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}

{"title":"Best proximity point theorems in metric spaces with property PC","authors":"S. Sadiq Basha","doi":"10.1007/s10474-026-01593-z","DOIUrl":"10.1007/s10474-026-01593-z","url":null,"abstract":"<div><p>In the article [S. Sadiq Basha, Best approximation theorems for almost cyclic contractions, J. Fixed Point Theory Appl. <b>23</b>, 32 (2021)], the author proved a best approximation theorem which ensures the existence of a best approximation for almost cyclic contractions in the richer framework of uniformly convex Banach space. Further, in the article [S. Sadiq Basha, Some best approximation theorems and best proximity point theorems, Acta Sci. Math. (Szeged) <b>89</b> (2023), 215-226], the author proved a best proximity point theorem which ascertains the existence of a best proximity point for almost cyclic contractions in the richer framework of uniformly convex Banach space. The purpose of this paper is to introduce a notion known as the property PC and extend the aforesaid best approximation theorem and best proximity point theorem to the less stringent framework of metric space with the property PC. As a consequence, the results obtained in this article generalize the well-renowned contraction principle due to Banach.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"178 1","pages":"40 - 51"},"PeriodicalIF":0.6,"publicationDate":"2026-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148285477","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}

{"title":"The Pompeiu problem and spherical spectral analysis","authors":"Michael J. Puls","doi":"10.1007/s10474-026-01592-0","DOIUrl":"10.1007/s10474-026-01592-0","url":null,"abstract":"<div><p>Let <i>K</i> be a compact subgroup of a locally compact group <i>G</i>. We investigate a Pompeiu type problem for homogeneous spaces <i>G</i>/<i>K</i>. Suppose <i>E</i> is a compact subset of <i>G</i>/<i>K</i>. Using recent work of László Székelyhidi on <i>K</i>-spectral analysis [L. Székelyhidi, Spherical spectral synthesis. Acta Math. Hungar. 153(1), 120–142 (2017)] we are able to give necessary and sufficient conditions for <i>E</i> to have the Pompeiu property when (<i>G</i>, <i>K</i>) is a Gelfand pair.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"178 1","pages":"27 - 39"},"PeriodicalIF":0.6,"publicationDate":"2026-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148285403","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}

{"title":"On the distribution of the Cantor-integers","authors":"Chun-Yun Cao,&nbsp;Jie Yu","doi":"10.1007/s10474-026-01588-w","DOIUrl":"10.1007/s10474-026-01588-w","url":null,"abstract":"<div><p>For any positive integer <span>(pge 3)</span>, let <i>A</i> be a proper subset of <span>({0,1,ldots , p-1})</span> with <span>({# }A=sge 2)</span>. Suppose <span>(h: {0,1,ldots ,s-1}rightarrow A)</span> is a strictly increasing one-to-one mapping. We focus on the so-called Cantor-integers <span>({a_n}_{nge 1})</span>, which consist of these positive integers <i>n</i> such that the digits of the <i>p</i>-ary expansion of <i>n</i> are taken solely from the elements of <i>A</i>. Evidently, the set <span>(mathfrak {C})</span> consisting of points <span>(xin [0,1])</span> such that the digits in the <i>p</i>-ary expansion of <i>x</i> are exclusively drawn from the elements of <i>A</i> is precisely the attractor of the iterated function system <span>({f_i}_{i=0}^{s-1})</span>, where <span>(f_i)</span> are functions defined on [0, 1] as <span>(f_i(x)=frac{x+h(i)}{p})</span>, respectively. Denote the classical self-similar measure supported on <span>(mathfrak {C})</span> by <span>(mu _{mathfrak {C}})</span> with <span>(mu _mathfrak {C}=sum _{i=0}^{s-1}frac{1}{s} mu _mathfrak {C}circ f_i^{-1})</span>. Note that <span>(n^{log _s p})</span> is the growth order of <span>(a_n)</span> and the set of accumulation points of the sequence <span>(left{ frac{a_n}{n^{log _s p}}:~nge 1right} )</span> is precisely the set <span>(left{ frac{x}{(mu _{mathfrak {C}}([0,x]))^{log _s p}}: xin mathfrak {C}cap [frac{h(1)}{p},1]right} )</span>. We show that this set is just an interval with the infimum <i>m</i> and supremum <i>M</i> of the sequence <span>(left{ frac{a_n}{n^{log _s p}}:~nge 1right} )</span> as its endpoints, in particular, <span>(left{ frac{x}{(mu _{mathfrak {C}}([0,x]))^{log _s p}}: xin mathfrak {C}backslash {0}right} =[m,M])</span> if <span>(0in A)</span>. Further, we show that the sequence <span>(left{ frac{a_n}{n^{log _s p}}right} _{nge 1})</span> is not uniformly distributed modulo 1, and it does not have cumulative distribution function, but has logarithmic distribution function (given by a specific Lebesgue integral). In the special case where <i>A</i> is the set composed of numbers from <span>({0,1,ldots , p-1})</span> that all have the same remainder of <i>r</i> when divided by some given positive integer <span>(q ge 2)</span> (i.e. <span>(h(x)=qx+r)</span>), we show that <span>(m=frac{q(s-1)+r}{p-1}, M=frac{q(p-1)+pr}{p-1})</span> .</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"178 1","pages":"1 - 26"},"PeriodicalIF":0.6,"publicationDate":"2026-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148285391","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}

{"title":"On the connection between games on a space and on its (C_p)-space","authors":"L. Chiozini","doi":"10.1007/s10474-025-01575-7","DOIUrl":"10.1007/s10474-025-01575-7","url":null,"abstract":"<div><p>We present a negative answer to Tkachuk's question if there is a Tychonoff space <i>X</i> such that <span>(C_p(X))</span> has the Fréchet–Urysohn property and Player II has a winning strategy in <span>(CD(C_p(X)))</span>, as well as a positive one to Clontz and Holshouser’s question whether there is a point-picking game on <span>(C_p(X))</span> which characterizes when <i>X</i> is not a Rothberger space. In reality, we prove a stronger statement: that there is a game on <span>(C_p(X))</span> which is equivalent to the Rothberger game on <i>X</i>. Moreover, we prove the equivalence between pairs of games, one of which played on <span>(C_p(X))</span> and one on <i>X</i>, by providing a two-way “translation” of strategies.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"177 2","pages":"326 - 338"},"PeriodicalIF":0.6,"publicationDate":"2026-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147682813","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}

{"title":"On the logarithmic calculus and Sidorenko's conjecture","authors":"X. Li,&nbsp;B. Szegedy","doi":"10.1007/s10474-026-01582-2","DOIUrl":"10.1007/s10474-026-01582-2","url":null,"abstract":"<div><p>We study a type of calculus for proving inequalities between subgraph densities that is based on Jensen's inequality for the logarithmic function.\u0000As a demonstration of the method we verify the conjecture of Erdös-Simonovits and Sidorenko for various families of graphs.\u0000In particular we give a short analytic proof for a result by Conlon, Fox and Sudakov. Using this, \u0000we prove the forcing conjecture for bipartite graphs in which one vertex is complete to the other side.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"177 2","pages":"450 - 463"},"PeriodicalIF":0.6,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-026-01582-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147682792","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}

{"title":"Concise proofs concerning the size and structure of large intersecting (k)-graphs","authors":"P. Frankl","doi":"10.1007/s10474-025-01547-x","DOIUrl":"10.1007/s10474-025-01547-x","url":null,"abstract":"<div><p>Let <span>(n &gt; 2k geq 4)</span> and let <span>(mathcal F subset {[n]choose k})</span> be an intersecting <span>(k)</span>-graph on <span>(n)</span> vertices, that is, <span>(Fcap F' neq emptyset)</span> for all <span>(F, F' in mathcal F)</span>.\u0000By the ErdH{o}s--Ko--Rado Theorem <span>(|mathcal F| leq { n - 1choose k - 1})</span> with equality holding only for the full-star, <span>(mathcal S_x)</span>, the family of all <span>(k)</span>-sets containing the vertex <span>(x)</span>.\u0000If we exclude stars, that is, subfamilies of <span>(mathcal S_x)</span> then <span>(|mathcal F| leq { n - 1choose k - 1} - { n - k - 1choose k - 1} + 1)</span> was proved by Hilton and Milner who determined the families attaining equality as well.\u0000Half a century later Han and Kohayakawa determined the next largest families.\u0000Then very recently Huang and Peng determined the fourth largest families.\u0000That is, they determined the largest families assuming that <span>(mathcal F)</span> is not a star and it is not contained neither in the Hilton--Milner families nor in the Han--Kohayakawa families.\u0000In the present paper we provide a unified simple proof for these two theorems as well as solve the corresponding problem for <span>(t )</span>-intersecting families <span>((|F cap F'| geq t))</span> albeit only for\u0000<span>(n &gt; t + max {4t(k - t + 1)^2, 2(t + 1)^2})</span>.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"177 2","pages":"247 - 264"},"PeriodicalIF":0.6,"publicationDate":"2026-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-025-01547-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147682799","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}