Mock modular forms with integral Fourier coefficients

  title={Mock modular forms with integral Fourier coefficients},
  author={Yingkun Li and Markus Schwagenscheidt},
  journal={Advances in Mathematics},
2 Citations

Deformations of Theta Integrals and A Conjecture of Gross-Zagier

In this paper, we complete the proof of Gross-Zagier’s conjecture concerning algebraicity of higher Green functions at a single CM point on the product of modular curves. The new ingredient is an

Higher Siegel theta lifts on Lorentzian lattices, harmonic Maass forms, and Eichler–Selberg type relations

. We investigate so-called “higher” Siegel theta lifts on Lorentzian lattices in the spirit of Bruinier–Ehlen–Yang and Bruinier–Schwagenscheidt. We give a series representation of the lift in terms



Harmonic Maass forms associated to real quadratic fields

In this paper, we explicitly construct harmonic Maass forms that map to the weight one theta series associated by Hecke to odd ray class group characters of real quadratic fields. From this

Petersson inner products of weight-one modular forms

  • M. Viazovska
  • Mathematics
    Journal für die reine und angewandte Mathematik (Crelles Journal)
  • 2019
In this paper we study the regularized Petersson product between a holomorphic theta series associated to a positive definite binary quadratic form and a weakly holomorphic weight-one modular form

q-series and weight 3/2 Maass forms

Abstract Despite the presence of many famous examples, the precise interplay between basic hypergeometric series and modular forms remains a mystery. We consider this problem for canonical spaces of

Traces of CM values of modular functions

Abstract Zagier proved that the traces of singular moduli, i.e., the sums of the values of the classical j-invariant over quadratic irrationalities, are the Fourier coefficients of a modular form of

Theta lifts for Lorentzian lattices and coefficients of mock theta functions

We evaluate regularized theta lifts for Lorentzian lattices in three different ways. In particular, we obtain formulas for their values at special points involving coefficients of mock theta

Spectacle cycles with coefficients and modular forms of half-integral weight

In this paper we present a geometric way to extend the Shintani lift from even weight cusp forms for congruence subgroups to arbitrary modular forms, in particular Eisenstein series. This is part of


In this paper we examine three examples of Ramanujan’s third order mock θ-functions and relate them to Rogers’ false θ-series and to a real-analytic modular form of weight 1/2.

On two geometric theta lifts

The theta correspondence has been an important tool in studying cycles in locally symmetric spaces of orthogonal type. In this paper we establish for the orthogonal group O(p,2) an adjointness result

Average CM-values of Higher Green's Function and Factorization

In this paper, we prove an averaged version of an algebraicity conjecture in \cite{GKZ87} concerning the values of higher Green's function at CM points. Furthermore, we give the factorization of the