MathematikaPub Date : 2026-04-01DOI: 10.1112/mtk.70088
Tomos Parry
{"title":"The -mean of the exponential sum of","authors":"Tomos Parry","doi":"10.1112/mtk.70088","DOIUrl":"10.1112/mtk.70088","url":null,"abstract":"<p>We use the classical circle method to give a relatively simple proof that\u0000\u0000 </p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147682877","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}
MathematikaPub Date : 2026-04-01DOI: 10.1112/mtk.70091
Bingrong Huang
{"title":"Mixed moments of Hecke eigenforms and -functions","authors":"Bingrong Huang","doi":"10.1112/mtk.70091","DOIUrl":"10.1112/mtk.70091","url":null,"abstract":"<p>In this paper, we establish estimates for the expectation and variance of the mixed (2,2)-moment of two Hecke eigenforms of distinct weights. Our results yield applications to triple product <span></span><math></math>-functions. The proofs are based on moments of <span></span><math></math>-functions.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147682876","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}
MathematikaPub Date : 2026-03-30DOI: 10.1112/mtk.70087
Robert Fraser
{"title":"Fourier decay of measures supported on sets of numbers with consecutive partial quotients belonging to a given set","authors":"Robert Fraser","doi":"10.1112/mtk.70087","DOIUrl":"10.1112/mtk.70087","url":null,"abstract":"<p>We consider measures supported on sets of irrational numbers possessing many consecutive partial quotients satisfying a condition based on the previous partial quotients. We show that under mild assumptions, such sets will always support measures whose Fourier transform decays to zero.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147665885","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}
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