{"title":"论 2 阶 L 函数的不变式，I：扭曲度与内移","authors":"J. Kaczorowski, A. Perelli","doi":"10.1142/s1793042124501215","DOIUrl":null,"url":null,"abstract":"This is the first part of a series of papers where the behaviour of the invariants under twist by Dirichlet characters is studied for $L$-functions of degree 2. Here we show, under suitable conditions, that degree and internal shift remain unchanged under twist. The ultimate goal of the series is to prove a general version of Weil converse theorem with minimal assumptions on the shape of the functional equation of the twists.","PeriodicalId":14293,"journal":{"name":"International Journal of Number Theory","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the invariants of L-functions of degree 2, I: Twisted degree and internal shift\",\"authors\":\"J. Kaczorowski, A. Perelli\",\"doi\":\"10.1142/s1793042124501215\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This is the first part of a series of papers where the behaviour of the invariants under twist by Dirichlet characters is studied for $L$-functions of degree 2. Here we show, under suitable conditions, that degree and internal shift remain unchanged under twist. The ultimate goal of the series is to prove a general version of Weil converse theorem with minimal assumptions on the shape of the functional equation of the twists.\",\"PeriodicalId\":14293,\"journal\":{\"name\":\"International Journal of Number Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-05-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Number Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s1793042124501215\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Number Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s1793042124501215","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the invariants of L-functions of degree 2, I: Twisted degree and internal shift
This is the first part of a series of papers where the behaviour of the invariants under twist by Dirichlet characters is studied for $L$-functions of degree 2. Here we show, under suitable conditions, that degree and internal shift remain unchanged under twist. The ultimate goal of the series is to prove a general version of Weil converse theorem with minimal assumptions on the shape of the functional equation of the twists.
期刊介绍：
This journal publishes original research papers and review articles on all areas of Number Theory, including elementary number theory, analytic number theory, algebraic number theory, arithmetic algebraic geometry, geometry of numbers, diophantine equations, diophantine approximation, transcendental number theory, probabilistic number theory, modular forms, multiplicative number theory, additive number theory, partitions, and computational number theory.
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