Acta Mathematica Hungarica最新文献

{"title":"Maximum mean discrepancies of Farey sequences","authors":"T. Karvonen,&nbsp;A. Zhigljavsky","doi":"10.1007/s10474-025-01577-5","DOIUrl":"10.1007/s10474-025-01577-5","url":null,"abstract":"<div><p>We identify a large class of positive-semidefinite kernels for which a certain polynomial rate of convergence of maximum mean discrepancies of Farey sequences is equivalent to the Riemann hypothesis. This class includes all Matérn kernels of order at least one-half.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"177 2","pages":"351 - 362"},"PeriodicalIF":0.6,"publicationDate":"2025-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147682701","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 (abc) conjecture implies infinitely many non-Wieferich places for fixed bases in number field","authors":"H. Graves,&nbsp;B. Weiss","doi":"10.1007/s10474-025-01563-x","DOIUrl":"10.1007/s10474-025-01563-x","url":null,"abstract":"<div><p>Silverman showed that, assuming the <span>(abc)</span> conjecture, there are <span>({gg} log x)</span> non-Wieferich primes base <span>( a)</span>\u0000 less than <span>(x)</span> [14], for all non-zero <span>(a)</span>. \u0000This inspired Graves and Murty [8], Chen and Ding [1,2], and then Ding [4] to find growth results,\u0000assuming the <span>(abc)</span> conjecture,\u0000 for non-Wieferich primes <span>(p)</span> base <span>( a)</span>, where <span>(p equiv 1 pmod{k})</span> for integers <span>(k geq 2)</span>. \u0000 In light of Murty, Srinivas, and Subramani's recent work on 'the Wieferich primes conjecture'\u0000and Euclidean algorithms in number fields [12], number theorists need results on non-Wieferich places in number fields.\u0000We prove analogues of the results of Graves and Murty and Ding, and show \u0000Ding's result holds for all bases <span>(a)</span> in all imaginary quadratic fields' rings of integers, with 31 explicitly listed exceptions.</p><p>Along the way, we generalize useful results on rational integers to algebraic integers.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"177 2","pages":"265 - 279"},"PeriodicalIF":0.6,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147682811","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":"A note on commutativity of the exponential spectrum in the operator algebra (mathcal{B}(ell^poplusell^q))","authors":"S. Daniel,&nbsp;A. Ghosh","doi":"10.1007/s10474-025-01571-x","DOIUrl":"10.1007/s10474-025-01571-x","url":null,"abstract":"<div><p>In a Banach algebra <span>(mathcal{A})</span>, for a pair of elements, the spectrum always commutes:\u0000</p><div><div><span>$$sigma(ab)setminus{0}=sigma(ba)setminus{0},$$</span></div></div><p> \u0000whereas the exponential spectrum does not, as shown by Klaja and Ransford. In literature, the operator algebra <span>(mathcal{B}(ell^poplusell^q))</span> was anticipated to be a potential algebra of the same type. But we have established that the exponential spectrum commutes in this algebra. This is achieved by proving that the exponential spectrum commutes in <span>(mathcal{B(X)})</span> if it commutes in the corresponding Calkin algebra.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"177 2","pages":"280 - 296"},"PeriodicalIF":0.6,"publicationDate":"2025-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147682812","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 multiplicities of interpoint distance","authors":"F. C. Clemen,&nbsp;A. Dumitrescu,&nbsp;D. Liu","doi":"10.1007/s10474-025-01562-y","DOIUrl":"10.1007/s10474-025-01562-y","url":null,"abstract":"<div><p>Given a set <span>(Xsubseteqmathbb{R}^2)</span> of <span>(n)</span> points and a distance <span>(d&gt;0)</span>, the multiplicity of <span>(d)</span> is the\u0000number of times the distance <span>(d)</span> appears between points in <span>(X)</span>. Let <span>(a_1(X) geq a_2(X) geq cdots geq a_m(X))</span> \u0000denote the multiplicities of the <span>(m)</span> distances determined by <span>(X)</span> and let\u0000<span>(a(X)=(a_1(X),dots,a_m(X)))</span>. In this paper, we study several\u0000questions from Erdős’s time regarding distance multiplicities. Among other results, we show that: \u0000</p><ul>\u0000 <li>\u0000 <p>(1) If <span>(X)</span> is convex or “not too convex”, then there exists a distance other than the diameter\u0000 that has multiplicity at most <span>(n)</span>.</p>\u0000 </li>\u0000 <li>\u0000 <p>(2) There exists a set <span>(Xsubseteqmathbb{R}^2)</span> of <span>(n)</span> points, such that many distances occur with high\u0000 multiplicity. In particular, at least <span>(n^{Omega(1/loglog{n})})</span> distances \u0000 have superlinear multiplicity in <span>(n)</span>.</p>\u0000 </li>\u0000 <li>\u0000 <p>(3) For any (not necessarily fixed) integer <span>(1leq kleqlog{n})</span>,\u0000 there exists <span>( {Xsubseteqmathbb{R}^2 } )</span> of <span>(n)</span> points, such that the difference between\u0000 the <span>(k^{text{th}})</span> and <span>((k+1)^{text{th}})</span> largest multiplicities is at least\u0000 <span>(Omega(frac{nlog{n}}{k}))</span>. \u0000 Moreover, the distances in <span>(X)</span> with the largest <span>(k)</span> multiplicities can be prescribed.</p>\u0000 </li>\u0000 <li>\u0000 <p>(4) For every <span>(nin N)</span>, there exists <span>(Xsubseteqmathbb{R}^2)</span> of <span>(n)</span> points, not all collinear or cocircular, such that <span>(a(X)= (n-1,n-2,ldots,1))</span>. There also exists <span>(Xsubseteqmathbb{R}^2)</span> of <span>(n)</span> points with pairwise distinct distance multiplicities and <span>(a(Y) neq (n-1,n-2,ldots,1))</span>.</p>\u0000 </li>\u0000 </ul></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"177 1","pages":"231 - 245"},"PeriodicalIF":0.6,"publicationDate":"2025-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-025-01562-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754329","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":"Analytic geometry and Hodge--Frobenius structure","authors":"X. Tong","doi":"10.1007/s10474-025-01568-6","DOIUrl":"10.1007/s10474-025-01568-6","url":null,"abstract":"<div><p>We study Frobenius structures in higher dimensional <i>p</i>-adic analytic geometry and the corresponding <i>p</i>-adic functional analysis. This will build up foundations for further study on some generalized cohomology of Frobenius modules and the corresponding generalized Iwasawa theory and generalized noncommutative Tamagawa number conjectures in the spirit of Burns--Flach--Fukaya--Kato and Nakamura (as well as certainly the original noncommutative Tamagawa number conjectures as observed by Pal--Zábrádi). We will work in the program proposed by Carter-Kedlaya--Zábrádi and after Pal--Zábrádi, and we will follow closely the approach from Kedlaya--Pottharst--Xiao to investigate the corresponding deformation of the generalized <i>p</i>-adic Hodge structures. </p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"177 1","pages":"193 - 230"},"PeriodicalIF":0.6,"publicationDate":"2025-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754282","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":"Some explicit results on the sum of a prime and an almost prime","authors":"D. R. Johnston,&nbsp;V. V. Starichkova","doi":"10.1007/s10474-025-01572-w","DOIUrl":"10.1007/s10474-025-01572-w","url":null,"abstract":"<div><p>Inspired by a classical result of Rényi, we prove that every even integer <span>(Ngeq 4)</span> can be written as the sum of a prime and a number with at most 395 prime factors. We also show,\u0000 under assumption of the generalised Riemann hypothesis, that this result can be improved to 31 prime factors. </p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"177 1","pages":"163 - 192"},"PeriodicalIF":0.6,"publicationDate":"2025-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754506","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":"Spectrogram analysis associated with the Whittaker convolution operators","authors":"S. Aledawish,&nbsp;F. Soltani","doi":"10.1007/s10474-025-01569-5","DOIUrl":"10.1007/s10474-025-01569-5","url":null,"abstract":"<div><p>As the harmonic analysis associated with the modified Whittaker transform has been extensively investigated and has witnessed a remarkable development, it is natural to study several aspects of the time-frequency analysis associated with the Whittaker convolution operators (WCO). Knowing the fact that the study of the time-frequency analysis is both theoretically interesting and practically useful, this article aims to explore two other aspects of time-frequency analysis associated with WCO, namely spectral analysis associated with concentration operators and spectrogram analysis. As an application, we obtain some results concerning the Whittaker heat operator and the Whittaker Poisson integral.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"177 1","pages":"103 - 123"},"PeriodicalIF":0.6,"publicationDate":"2025-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754320","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":"Inverse problems of subsequence sums related to the support of sequences in finite abelian groups","authors":"H. Chao,&nbsp;J. He,&nbsp;J. Peng,&nbsp;Z. Wang,&nbsp;Y. Yang","doi":"10.1007/s10474-025-01570-y","DOIUrl":"10.1007/s10474-025-01570-y","url":null,"abstract":"<div><p>Let <span>(G)</span> be a finite abelian group and <span>(S)</span> a sequence with elements of <span>(G)</span>. Let <span>(|S|)</span> denote the length of <span>(S)</span> and <span>(mathrm{supp}(S))</span> the set of all the distinct terms in <span>(S)</span>. Let <span>(Sigma(S))</span> denote the set of group elements which can be expressed as a sum of a nonempty subsequence of <span>(S)</span>. It is known that if <span>({0notinSigma(S)})</span>, then <span>(|Sigma(S)| geq |S|+|mathrm{supp}(S)|-1)</span>. The sequence <span>(S)</span> satisfying \u0000<span>(0notinSigma(S))</span>\u0000 and <span>(|Sigma(S)| = |S| + |mathrm{supp}(S)| - 1)</span>\u0000 has been described.\u0000 In this paper, we determine the sequence <span>(S)</span> with <span>(0notinSigma(S))</span>\u0000 such that <span>(|Sigma(S)|=|S|+|mathrm{supp}(S)|)</span>\u0000.\u0000 As a consequence, we obtain some new results on the sequence <span>(S)</span>\u0000 with <span>(0notinSigma_{|G|}(S))</span>\u0000 and <span>(|Sigma_{|G|}(S)|=|S|-|G|+|mathrm{supp}(S)|-1)</span>\u0000,\u0000 where <span>(Sigma_{|G|}(S))</span>\u0000 denotes the set of group elements which can be expressed as a sum of a subsequence of <span>(S)</span>\u0000 of length <span>(|G|)</span>\u0000.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"177 1","pages":"124 - 139"},"PeriodicalIF":0.6,"publicationDate":"2025-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754321","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":"Congruences and density results for partitions into distinct even parts","authors":"H. Nath,&nbsp;A. Sarma","doi":"10.1007/s10474-025-01573-9","DOIUrl":"10.1007/s10474-025-01573-9","url":null,"abstract":"<div><p>We consider the set of partitions \u0000<span>( ped (n))</span> which counts the number of partitions of <span>(n)</span> wherein the even parts are distinct (and the odd parts are unrestricted). Using an algorithm developed by Radu, we prove congruences modulo 192 which were conjectured by Nath \u0000[10]. \u0000Further, we prove a few infinite families of congruences modulo 24 by using a result of Newman. Also, we prove that \u0000<span>(ped (9n+7))</span> is lacunary modulo \u0000<span>(2^{k+2}cdot 3)</span> and \u0000<span>(3^{k+1}cdot 4)</span> for all positive integers <span>(kgeq0)</span>. We further prove an infinite family of congruences for <span>(ped (n))</span> modulo arbitrary powers of 2 by employing a result of Ono and Taguchi on the nilpotency of Hecke operators.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"177 1","pages":"140 - 162"},"PeriodicalIF":0.6,"publicationDate":"2025-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754319","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":"Resolvability in products and squares","authors":"A. E. Lipin","doi":"10.1007/s10474-025-01565-9","DOIUrl":"10.1007/s10474-025-01565-9","url":null,"abstract":"<div><p>Suppose <span>(X)</span> and <span>(Y)</span> are topological spaces, <span>(|X| = Delta(X))</span> and <span>(|Y| = Delta(Y))</span>. We investigate resolvability of the product <span>(X times Y)</span>. We prove that: \u0000</p><ul>\u0000 <li>\u0000 <p>I. If <span>(|X| = |Y| = omega)</span> and <span>(X,Y)</span> are Hausdorff, then <span>( { X times Y } )</span> is maximally resolvable.</p>\u0000 </li>\u0000 <li>\u0000 <p>II. If <span>(2^kappa = kappa^+)</span>, <span>({|X|, mathrm{cf}|X|} cap {kappa, kappa^+} ne emptyset)</span> and <span>(mathrm{cf}|Y| = kappa^+)</span>, then the space <span>({ X times Y})</span> is <span>(kappa^+)</span>-resolvable. \u0000In particular, under GCH the space <span>(X^2)</span> is <span>(mathrm{cf}|X|)</span>-resolvable whenever <span>(mathrm{cf}|X|)</span> is an isolated cardinal.</p>\u0000 </li>\u0000 <li>\u0000 <p>III. (<span>(mathfrak{r} = mathfrak{c})</span>) If <span>(mathrm{cf}|X| = omega)</span> and <span>({rm cf}|Y| = {rm cf}(mathfrak{c}))</span>, then the space <span>( { X times Y } )</span> is <span>(omega)</span>-resolvable. \u0000If, moreover, <span>({rm cf}(mathfrak{c}) = omega_1)</span>, then the space <span>( { X times Y } )</span> is <span>(omega_1)</span>-resolvable.</p>\u0000 </li>\u0000 </ul></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"177 1","pages":"64 - 72"},"PeriodicalIF":0.6,"publicationDate":"2025-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145754406","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}