An analogue of Weil’s converse theorem for harmonic Maass forms of polynomial growth

被引：0
作者：
Karam Deo Shankhadhar
Ranveer Kumar Singh
机构：
[1] Indian Institute of Science Education and Research Bhopal,Department of Mathematics
[2] Rutgers University,NHETC, Department of Physics and Astronomy
来源：
Research in Number Theory | 2022年 / 8卷
关键词：
Harmonic Maass forms; Differential operators; Dirichlet series; Converse theorem; Primary 11F12; 11F25; Secondary 11F66; 11M36;
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摘要：
We construct a family of harmonic Maass forms of polynomial growth of any level corresponding to any cusp whose shadows are Eisenstein series of integral weight. We further consider Dirichlet series attached to a harmonic Maass form of polynomial growth, study its analytic properties, and prove an analogue of Weil’s converse theorem.
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