{"title":"通过积分表示的谱互易性","authors":"Ramon M. Nunes","doi":"10.2140/ant.2023.17.1381","DOIUrl":null,"url":null,"abstract":"<p>We prove a spectral reciprocity formula for automorphic forms on <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi> GL</mi><mo> <!--FUNCTION APPLICATION--> </mo><!--nolimits--><mo stretchy=\"false\">(</mo><mn>2</mn><mo stretchy=\"false\">)</mo></math> over a number field that is reminiscent of one found by Blomer and Khan. Our approach uses period representations of <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>L</mi></math>-functions and the language of automorphic representations. </p>","PeriodicalId":50828,"journal":{"name":"Algebra & Number Theory","volume":"55 3","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Spectral reciprocity via integral representations\",\"authors\":\"Ramon M. Nunes\",\"doi\":\"10.2140/ant.2023.17.1381\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We prove a spectral reciprocity formula for automorphic forms on <math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mi> GL</mi><mo> <!--FUNCTION APPLICATION--> </mo><!--nolimits--><mo stretchy=\\\"false\\\">(</mo><mn>2</mn><mo stretchy=\\\"false\\\">)</mo></math> over a number field that is reminiscent of one found by Blomer and Khan. Our approach uses period representations of <math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mi>L</mi></math>-functions and the language of automorphic representations. </p>\",\"PeriodicalId\":50828,\"journal\":{\"name\":\"Algebra & Number Theory\",\"volume\":\"55 3\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-08-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra & Number Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2140/ant.2023.17.1381\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra & Number Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2140/ant.2023.17.1381","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
We prove a spectral reciprocity formula for automorphic forms on over a number field that is reminiscent of one found by Blomer and Khan. Our approach uses period representations of -functions and the language of automorphic representations.
期刊介绍：
ANT’s inclusive definition of algebra and number theory allows it to print research covering a wide range of subtopics, including algebraic and arithmetic geometry. ANT publishes high-quality articles of interest to a broad readership, at a level surpassing all but the top four or five mathematics journals. It exists in both print and electronic forms.
The policies of ANT are set by the editorial board — a group of working mathematicians — rather than by a profit-oriented company, so they will remain friendly to mathematicians'' interests. In particular, they will promote broad dissemination, easy electronic access, and permissive use of content to the greatest extent compatible with survival of the journal. All electronic content becomes free and open access 5 years after publication.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
