We construct a family of examples of harmonic Maass forms of polynomial
growth for any level 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.Comment: 28 Page

Shankhadhar, Karam Deo

Singh, Ranveer Kumar

English

arXiv

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.Comment: After referee reports, the article has been revised significantly.
  The main theorem and its proof have been corrected. To appear in Research in
  Number Theor

An Analogue of Weil's Converse Theorem for Harmonic Maass Forms of Polynomial Growth

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