Directly to content
  1. Publishing |
  2. Search |
  3. Browse |
  4. Recent items rss |
  5. Open Access |
  6. Jur. Issues |
  7. DeutschClear Cookie - decide language by browser settings

Contributions to the theory of modular forms and L-functions

Franke, Johann

[img]
Preview
PDF, English
Download (1MB) | Terms of use

Citation of documents: Please do not cite the URL that is displayed in your browser location input, instead use the DOI, URN or the persistent URL below, as we can guarantee their long-time accessibility.

Abstract

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.

Item Type: Dissertation
Supervisor: Kohnen, Prof. Dr. Winfried
Place of Publication: Heidelberg
Date of thesis defense: 10 September 2020
Date Deposited: 17 Sep 2020 09:07
Date: 2020
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Mathematics
Subjects: 510 Mathematics
Controlled Keywords: Modular forms, L-functions, Period polynomials
About | FAQ | Contact | Imprint |
OA-LogoDINI certificate 2013Logo der Open-Archives-Initiative