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Dissertation
Moments of L-functions associated with Maass forms
Washington State University
Doctor of Philosophy (PhD), Washington State University
01/2022
DOI:
https://doi.org/10.7273/000004401
Handle:
https://hdl.handle.net/2376/124942
Abstract
In this thesis we present the requisite building blocks to study and discuss aspects of modern analytic number theory, in this case the study of automorphic forms, in particular Maass forms and their L-functions.We give an overview of and background on these notions without being overly technical.
Using this background we compute, using spectral theory for GL(2) and GL(3), asymptotic formulas for moments of GL(3)×GL(2) L-functions and their derivatives at the central point, twisted by GL(2) Hecke eigenvalues at primes.We use this to show that self-dual GL(3) Hecke--Maass cusp forms are uniquely determined by the central values L'(1/2, f × u_j) where u_j is a sequence of odd Hecke--Maass forms for GL(2) with large Laplacian eigenvalues.
We also show that infinitely many of these derivatives are nonvanishing at the central point.
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Details
- Title
- Moments of L-functions associated with Maass forms
- Creators
- Jakob Erik Alexander Streipel
- Contributors
- Sheng-Chi Liu (Advisor)Matthew Hudelson (Committee Member)Judi McDonald (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Mathematics and Statistics, Department of
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Publisher
- Washington State University
- Number of pages
- 110
- Identifiers
- 99900883237401842
- Language
- English
- Resource Type
- Dissertation