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On small divisor functions and a construction of polar harmonic Maass forms

Posted in
Speaker: 
Andreas Mono
Zugehörigkeit: 
Universität zu Köln
Datum: 
Mit, 2021-02-10 14:30 - 15:30
Parent event: 
Number theory lunch seminar

Zoom Meeting ID: 919 6497 4060
For password see the email or contact Pieter Moree (moree@mpim...).

 

Recently, Mertens, Ono, and Rolen studied mock modular analogues of Eisenstein series. Their coefficients are given by small divisor functions, and have shadows given by classical Shimura theta functions. Here, we construct a second class of small divisor functions, and prove that these generate the holomorphic part of polar harmonic (weak) Maaß forms of weight 32 .
Specializing to a certain choice of parameters, we obtain an identity between our small divisor function and Hurwitz class numbers. Lastly, we present p-adic congruences of our polar (weak) harmonic Maaß form, when p is an odd prime. This is joint work with
Joshua Males and Larry Rolen.

 

 

 

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