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CC BY-NC-SA V4.0, Open Access
Dissertation
THE M-TH SYMMETRIC POWER L-FUNCTION ANALOG OF SELBERG’S RESULTS ON S(T)
Washington State University
Doctor of Philosophy (PhD), Washington State University
01/2021
DOI:
https://doi.org/10.7273/000001855
Handle:
https://hdl.handle.net/2376/120412
Abstract
Let $L(\textup{sym}^m,f)$ be the $m$-th symmetric power $L$-function associated with a cusp form $f$ and $S_f^{(m)}(t)=\frac{1}{\pi}\arg L(\textup{sym}^mf,\frac{1}{2}+it)$. In this case, we investigate $S_f^{(m)}(t)$ to establish an asymptotic formula of the moments of $S_f^{(m)}(t)$. In last chapter, we also investigate $S_k^{(m)}(t)=\frac{1}{\pi}\arg L(\textup{sym}^mf_k,\frac{1}{2}+it)$ where $L(\textup{sym}^mf_k,\frac{1}{2}+it)$ is the $m$-th symmetric power $L$-function associated with a Hecke-Maass form $f_k$ to establish a similar asymptotic formula of the moments of $S_k^{(m)}(t)$ for $k<5$.
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Details
- Title
- THE M-TH SYMMETRIC POWER L-FUNCTION ANALOG OF SELBERG’S RESULTS ON S(T)
- Creators
- Jemin Shim
- Contributors
- Sheng-Chi Liu (Advisor)Judith McDonald (Committee Member)Michael Tsatsomeros (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
- 61
- Identifiers
- 99900606550001842
- Language
- English
- Resource Type
- Dissertation