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On a Divisor Modular Form and a Theta Lift (2509.01378v1)
Published 1 Sep 2025 in math.NT
Abstract: In 1975, Zagier introduced the highly influential hyperbolic Poincar\'e series $f_{k,D}$. We connect the divisor modular form of $f_{k,D}$ to a new weak Maass form $\omega_{k+1,D}$. Furthermore, we show that the generating function of $\omega_{k+1,D}$ 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.
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