title: Contributions to the theory of modular forms and L-functions
creator: Franke, Johann
subject: ddc-510
subject: 510 Mathematics
description: In this thesis we present a new method to construct modular forms using rational functions. It relies on contour integration and Weil's converse theorem. We give several applications, reaching from a relation between cotangent sums and $L$-functions, formulas for Eichler integrals and period polynomials and series representations for $L$-functions corresponding to products of Eisenstein series. \\  With similar ideas, based on contour integration, we move on to equations which were originally studied by Ramanujan and generalize his formulas to those containing $L$-functions at rational arguments. We work out a very general framework for finding new equations of the Ramanujan type that can be applied to a wide range of $L$-functions.
date: 2020
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/28845/1/Diss_neu_Abgabe.pdf
identifier: DOI:10.11588/heidok.00028845
identifier: urn:nbn:de:bsz:16-heidok-288451
identifier:   Franke, Johann  (2020) Contributions to the theory of modular forms and L-functions.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/28845/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng