{"title":"L-Series for Vector-Valued Weakly Holomorphic Modular Forms and Converse Theorems","authors":"Subong Lim, Wissam Raji","doi":"arxiv-2409.04258","DOIUrl":null,"url":null,"abstract":"We introduce the $L$-series of weakly holomorphic modular forms using Laplace\ntransforms and give their functional equations. We then determine converse\ntheorems for vector-valued harmonic weak Maass forms, Jacobi forms, and\nelliptic modular forms of half-integer weight in Kohnen plus space.","PeriodicalId":501064,"journal":{"name":"arXiv - MATH - Number Theory","volume":"103 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Number Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.04258","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We introduce the $L$-series of weakly holomorphic modular forms using Laplace
transforms and give their functional equations. We then determine converse
theorems for vector-valued harmonic weak Maass forms, Jacobi forms, and
elliptic modular forms of half-integer weight in Kohnen plus space.