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

Abstract

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.

arXiv commentAfter referee reports, the article has been revised significantly. The main theorem and its proof have been corrected. To appear in Research in Number Theory