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An Analogue of Weil's Converse Theorem for Harmonic Maass Forms of Polynomial Growth
Karam Deo Shankhadhar, Ranveer Kumar Singh
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 conside…
Zagier's weight mock modular form
Ajit Bhand, Ranveer Kumar Singh
Mock modular forms have their origins in Ramanujan's pioneering work on mock theta functions. In a 1975 paper, Zagier proved certain transformation properties of the generating fun…
Isomorphism of Skew-Holomorphic Harmonic Maass-Jacobi Forms and Certain Weak Harmonic Maass Forms
Ranveer Kumar Singh
Recently Bringmann, Raum and Richter generalised the definition of Jacobi forms and Skoruppa's skew-holomorphic Jacobi forms by intertwining with harmonic Maass forms. We prove the…
Maass lifts of half-integral weight Eisenstein series and theta powers
Ajit Bhand, Karam Deo Shankhadhar, Ranveer Kumar Singh
In this paper, we explicitly construct mock modular forms whose shadows are Eisenstein series of arbitrary integral and half-integral weight, level and character at the cusps $\inf…