On a Divisor Modular Form and a Theta Lift

Abstract

In 1975, Zagier introduced the highly influential hyperbolic Poincaré series $f_{k,D}$. We connect the divisor modular form of $f_{k,D}$ to a new weak Maass form $\ddot{I}{‰}_{k+1,D}$. Furthermore, we show that the generating function of $\ddot{I}{‰}_{k+1,D}$ has the same modularity properties as Kohnen and Zagier's fruitful theta kernel generating the $f_{k,D}$'s. This yields a new theta lift.

14 pages, comments welcome