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Murmurations via Petersson trace formula 通过Petersson轨迹公式的杂音
IF 0.6 3区 数学
Mathematika Pub Date : 2026-10-14 DOI: 10.1112/mtk.70135
Chan Ieong Kuan, Didier Lesesvre
{"title":"Murmurations via Petersson trace formula","authors":"Chan Ieong Kuan,&nbsp;Didier Lesesvre","doi":"10.1112/mtk.70135","DOIUrl":"https://doi.org/10.1112/mtk.70135","url":null,"abstract":"<p>We prove the murmuration phenomenon, which is a correlation between signs of functional equations and Fourier coefficients, in the case of modular forms in the weight aspect. We in particular improve the range of visibility of murmurations compared to previous results. This is the first approach to the murmuration phenomenon using a relative trace formula, showing its robustness.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70135","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205854","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
Incompleteness of the Ewald–Shephard space of asymmetry classes 不对称类的Ewald-Shephard空间的不完备性
IF 0.6 3区 数学
Mathematika Pub Date : 2026-10-13 DOI: 10.1112/mtk.70134
Dong Qiu, Yixia Wu, Xingyu Zhang
{"title":"Incompleteness of the Ewald–Shephard space of asymmetry classes","authors":"Dong Qiu,&nbsp;Yixia Wu,&nbsp;Xingyu Zhang","doi":"10.1112/mtk.70134","DOIUrl":"https://doi.org/10.1112/mtk.70134","url":null,"abstract":"<p>This paper answers a long-standing open problem concerning the completeness of the metric space of asymmetry classes introduced by Ewald and Shephard (1966). We prove that this metric space is <i>incomplete</i> for <span></span><math></math>. Our approach reveals that the Ewald–Shephard metric <span></span><math></math> is equivalent to a quotient metric on a certain function space of odd continuous functions modulo linear functions, and that the Lipschitz regularity of odd parts of support functions constitutes an essential obstruction to completeness. We explicitly construct a Cauchy sequence of asymmetry classes whose limit cannot be represented by any compact convex body, thereby rigorously establishing the incompleteness of the space.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205325","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
Wasserstein rigidity over with smooth norms 瓦瑟斯坦刚性与平滑规范
IF 0.6 3区 数学
Mathematika Pub Date : 2026-10-05 DOI: 10.1112/mtk.70132
Zoltán M. Balogh, Eric Ströher, Tamás Titkos, Dániel Virosztek
{"title":"Wasserstein rigidity over with smooth norms","authors":"Zoltán M. Balogh,&nbsp;Eric Ströher,&nbsp;Tamás Titkos,&nbsp;Dániel Virosztek","doi":"10.1112/mtk.70132","DOIUrl":"https://doi.org/10.1112/mtk.70132","url":null,"abstract":"<p>We study <span></span><math></math> spaces <span></span><math></math> over <span></span><math></math> equipped with a norm metric <span></span><math></math>. We show that, if the norm is smooth enough, then the Wasserstein space is isometrically rigid whenever <span></span><math></math>. We also show that, even when <span></span><math></math>, we can recover the isometric rigidity of the Wasserstein space <span></span><math></math> when <span></span><math></math> is an <span></span><math></math> and <span></span><math></math>.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70132","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149145798","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
Towards the Erdős matching conjecture for 4-uniform hypergraphs: Stability and applications 关于4-一致超图的Erdős匹配猜想：稳定性与应用
IF 0.6 3区 数学
Mathematika Pub Date : 2026-10-05 DOI: 10.1112/mtk.70133
Peter Frankl, Hongliang Lu, Jie Ma, Yuze Wu
{"title":"Towards the Erdős matching conjecture for 4-uniform hypergraphs: Stability and applications","authors":"Peter Frankl,&nbsp;Hongliang Lu,&nbsp;Jie Ma,&nbsp;Yuze Wu","doi":"10.1112/mtk.70133","DOIUrl":"https://doi.org/10.1112/mtk.70133","url":null,"abstract":"<p>A famous conjecture of Erdős asserts that for <span></span><math></math>, the maximum number of edges in an <span></span><math></math>-vertex <span></span><math></math>-uniform hypergraph without <span></span><math></math> pairwise disjoint edges is <span></span><math></math>. This problem has been central in extremal combinatorics, with substantial progress in the literature, including a complete solution for <span></span><math></math> due to the first author. In this paper, we make progress towards the 4-uniform case, proving the conjecture for <span></span><math></math> and sufficiently large <span></span><math></math>, thereby taking a first step analogous to the 3-uniform case. The main technical contribution is a stability result of independent interest. We further apply this stability to resolve two new instances of conjectures on the minimum <span></span><math></math>-degree threshold for matchings in 5- and 6-uniform hypergraphs, in a strengthened form.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149145565","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
Extreme values of class group -functions 类群函数的极值
IF 0.6 3区 数学
Mathematika Pub Date : 2026-09-30 DOI: 10.1112/mtk.70131
João C. C. Vargas
{"title":"Extreme values of class group -functions","authors":"João C. C. Vargas","doi":"10.1112/mtk.70131","DOIUrl":"https://doi.org/10.1112/mtk.70131","url":null,"abstract":"<p>We give a lower bound for the maximum value of class group <span></span><math></math>-functions attached to <span></span><math></math> at the central point and show that this value is on average at least\u0000\u0000 </p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149147011","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
Graph-null sets Graph-null集
IF 0.6 3区 数学
Mathematika Pub Date : 2026-09-28 DOI: 10.1112/mtk.70130
M. Laczkovich, A. Máthé
{"title":"Graph-null sets","authors":"M. Laczkovich,&nbsp;A. Máthé","doi":"10.1112/mtk.70130","DOIUrl":"https://doi.org/10.1112/mtk.70130","url":null,"abstract":"<p>We say that a plane set <span></span><math></math> is <i>graph-null</i>, if there is a function <span></span><math></math> such that <span></span><math></math>. A plane set <span></span><math></math> has the <i>translational Kakeya property</i> if, for every translated copy <span></span><math></math> of <span></span><math></math> and for every <span></span><math></math>, there is a finite sequence of vertical and horizontal translations bringing <span></span><math></math> to <span></span><math></math> such that the area touched during the horizontal translations is less than <span></span><math></math>. These properties are equivalent if <span></span><math></math> is compact. We show that the graph of every absolutely continuous function is graph-null. Also, the graph of a typical continuous function is graph-null. Therefore, there are nowhere differentiable continuous functions whose graphs are graph-null. Still, we show that there exists a continuous function whose graph is not graph-null.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70130","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149146769","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
An effective Bombieri–Vinogradov error term for sifting problems 筛选问题的有效Bombieri-Vinogradov误差项
IF 0.6 3区 数学
Mathematika Pub Date : 2026-09-10 DOI: 10.1112/mtk.70129
Daniel R. Johnston
{"title":"An effective Bombieri–Vinogradov error term for sifting problems","authors":"Daniel R. Johnston","doi":"10.1112/mtk.70129","DOIUrl":"https://doi.org/10.1112/mtk.70129","url":null,"abstract":"<p>In number theory, many major results related to the additive properties of primes are proven using the methods of sieve theory. However, in nearly every case, the existing proofs of these results are ineffective, in that explicit values for which they hold cannot be computed. The reason for this ineffectivity is the reliance on the Bombieri–Vinogradov theorem. In this paper, we show that any classical sifting problem with a Bombieri–Vinogradov style error term can, in fact, be made effective, with no loss to the asymptotic form of the original (ineffective) result. This is done by carefully modifying the sieve upper and lower bounds to avoid the usual complications regarding Siegel zeros. We also provide some simple applications. For example, we show that one may effectively bound the number of primes <span></span><math></math> such that <span></span><math></math> is also prime by\u0000\u0000 </p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70129","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942929","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
Pair correlation conjecture for the zeros of the Riemann zeta-function I: Simple and critical zeros 黎曼函数I零点的对相关猜想：简单零和临界零
IF 0.6 3区 数学
Mathematika Pub Date : 2026-09-09 DOI: 10.1112/mtk.70127
Daniel A. Goldston, Junghun Lee, Jordan Schettler, Ade Irma Suriajaya
{"title":"Pair correlation conjecture for the zeros of the Riemann zeta-function I: Simple and critical zeros","authors":"Daniel A. Goldston,&nbsp;Junghun Lee,&nbsp;Jordan Schettler,&nbsp;Ade Irma Suriajaya","doi":"10.1112/mtk.70127","DOIUrl":"https://doi.org/10.1112/mtk.70127","url":null,"abstract":"<p>Montgomery in 1973 introduced the pair correlation conjecture (PCC) for zeros of the Riemann zeta-function. He also conjectured that asymptotically 100% of the zeros are simple. His reasoning to support these two conjectures used the Riemann hypothesis (RH). Building on Montgomery's approach, Gallagher and Mueller proved in 1978 that PCC under RH implies that 100% of the zeros are simple. Actually, the method of Gallagher and Mueller does not depend on RH, and thus Montgomery's second simplicity conjecture follows from his PCC conjecture without additionally assuming RH. We clarify this result by explicitly not assuming RH and considering PCC as a conjecture only concerning the vertical distribution of zeros. We then show that, for the first time, PCC can also be used to obtain information on the horizontal distribution of zeros. Using Gallagher and Mueller's method and a new idea concerning “horizontal multiplicity,” we use PCC to prove that asymptotically 100% of the zeros are not only simple but also on the critical line.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942634","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
How to pick your football team 如何选择你的足球队
IF 0.6 3区 数学
Mathematika Pub Date : 2026-09-01 DOI: 10.1112/mtk.70128
Bhargav Narayanan
{"title":"How to pick your football team","authors":"Bhargav Narayanan","doi":"10.1112/mtk.70128","DOIUrl":"https://doi.org/10.1112/mtk.70128","url":null,"abstract":"<p>Team captains Alice and Bob divide up <span></span><math></math> footballers, each reduced to a real-valued score, into two teams of <span></span><math></math> footballers each. On each turn, one captain plays <i>picker</i>, and the other <i>chooser</i>: the picker names a footballer yet to be selected, and the chooser decides which captain's team receives that footballer. Alice starts as picker, Bob as chooser, and the roles alternate. As soon as either captain has a full team of <span></span><math></math> footballers, the other captain receives all remaining footballers, and the team with the larger sum of scores wins. Settling a problem raised by Eccles in 2015, we show that Alice cannot win.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70128","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942267","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
On the behaviour of cycle integrals of invariant 关于不变量循环积分的性质
IF 0.6 3区 数学
Mathematika Pub Date : 2026-08-22 DOI: 10.1112/mtk.70124
Balesh Kumar, Jashoda Kumari
{"title":"On the behaviour of cycle integrals of invariant","authors":"Balesh Kumar,&nbsp;Jashoda Kumari","doi":"10.1112/mtk.70124","DOIUrl":"https://doi.org/10.1112/mtk.70124","url":null,"abstract":"<p>In this paper, we study the values of modular functions at real quadratic irrationalities which are defined in terms of cycle integrals of modular functions associated with closed geodesics. We refine a result of Bengoechea and Imamog̎lu to include values (and its limiting behaviour) of modular functions at a larger class of real quadratic irrationalities. As a consequence, we deduce the limiting behaviour of values of modular functions at powers of Pisot–Vijayaraghavan numbers. Further, we deduce distribution of class numbers of real quadratic fields having discriminants of a particular type.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148785201","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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