Locally harmonic Maaß forms of positive even weight

Abstract

We twist Zagier's function $f_{k,D}$ by a sign function and a genus character. Assuming weight $0<k\equiv 2(\mathrm{mod}4)$, and letting $D$ be a positive non-square discriminant, we prove that the obstruction to modularity caused by the sign function can be corrected obtaining a locally harmonic Maaßform or a local cusp form of the same weight. In addition, we provide an alternative representation of our new function in terms of a twisted trace of modular cycle integrals of a Poincaré series due to Petersson.

17 pages, no figures

References in corpus (6)

• On a completed generating function of locally harmonic Maass forms
• On cycle integrals of weakly holomorphic modular forms
• Meromorphic modular forms with rational cycle integrals
• A problem of Petersson about weight 0 meromorphic modular forms
• Identities of Cycle Integrals of Weak Maass Forms
• Central $L$-values of elliptic curves and local polynomials

Cited by in corpus (2)

• Flipping operators and locally harmonic Maass forms
• A modular framework for functions of Knopp and indefinite binary quadratic forms