Date of Submission
4-23-2025
Date of Award
10-13-2025
Institute Name (Publisher)
Indian Statistical Institute
Document Type
Doctoral Thesis
Degree Name
Doctor of Philosophy
Subject Name
Mathematics
Department
Theoretical Statistics and Mathematics Unit (TSMU-Kolkata)
Supervisor
Munshi, Ritabrata
Abstract (Summary of the Work)
Let $F$ be a Hecke-Maa\ss\ cusp form for $SL(3,\mathbb{Z})$. In this dissertation, we obtain a non-trivial upper bound of the second moment of $L(F,s)$ in the $t$-aspect: $$ \int_{T}^{2T}|L(F,1/2+it)|^2 dt\ll_{F,\epsilon} T^{3/2-3/32+\epsilon}.$$ Immediate corollaries include improvements over the existing results on the Subconvexity bound for self-dual $GL(3)$ $L$-functions in the $t$-aspect and for self-dual $GL(3)\times GL(2)$ $L$-functions in the $GL(2)$ spectral aspect, the error term in the Rankin-Selberg problem, and the zero density estimate for $GL(3)$ $L$-functions.
Control Number
TH657
DOI
https://dspace.isical.ac.in/items/1e15874d-bd80-415d-9a12-d10cd525d509
DSpace Identifier
http://hdl.handle.net/10263/7619
Recommended Citation
Pal, Sampurna, "Second Moment of Degree Three L-Functions" (2025). Doctoral Theses. 655.
https://digitalcommons.isical.ac.in/doctoral-theses/655