Arithmetic and analytical aspects of Siegel modular forms

by Fabian Waibel
Doctoral thesis
Date of Examination:2020-06-25
Date of issue:2020-09-24
Advisor:Prof. Dr. Valentin Blomer
Referee:Prof. Dr. Valentin Blomer
Referee:Prof. Dr. Jörg Brüdern
Persistent Address: http://dx.doi.org/10.53846/goediss-8208

 

 

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Abstract

English

This dissertation treats various topics in the theory of Siegel modular forms on congruence subgroups of large level. In the first part, we compute a second moment of the spinor L-function at the central point and give applications to non-vanishing. Then, we establish an asymptotic formula for the number of representations of a binary quadratic form by an integral quadratic form of rank ≥ 12. Along the way, we improve previous bounds for the classical theta series and give uniform bounds for the Fourier coefficients of Klingen-Eisenstein series.
Keywords: Modular forms; Theta series; Eisenstein series; Quadratic forms
 
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