Fourier coefficients of kernels of casp forms.
Lead Research Organisation:
University of Nottingham
Department Name: Sch of Mathematical Sciences
Abstract
A basic question in analytic number theory is the arithmetic of special values of L-functions associated to cusp forms. One of the methods towards its resolution is based on kernels of L-functions in terms of the Petersson scalar product. In particular, the Fourier coefficients of such kernels can lead to important information about the structure of special values of L-functions. We aim to investigate the explicit form of those Fourier coefficients.
Organisations
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N50970X/1 | 01/10/2016 | 30/09/2021 | |||
| 1946566 | Studentship | EP/N50970X/1 | 01/10/2017 | 28/10/2020 | Joshua Drewitt |
| Description | An in-depth investigation of the so-called real analytic modular forms introduced by Francis Brown a few years ago. The main aim was to study the classical number theoretic properties of real-analytic forms, including L-functions, periods associated to real-analytic modular forms and arithmetic properties of "critical values" of such L-functions. The first set of such aims has already been achieved and some of the findings are included in a paper (co-authored with N. Diamantis) currently under peer review for a major journal. |
| Exploitation Route | Further work on subtler questions of Brown's programme is currently under way. This work builds on the already completed part of the project. The main beneficiaries of this work is other researchers working in the broader area of modular forms and analytic number theory |
| Sectors | Education,Other |
| URL | https://arxiv.org/abs/1907.02895 |