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The second moment of the $GL_3$ standard $L$-function on the critical line
- Publication Year :
- 2024
-
Abstract
- We obtain a strong bound on the second moment of the $GL_3$ standard $L$-function on the critical line. The method builds on the recent work of Aggarwal, Leung, and Munshi which treated shorter intervals. We deduce some corollaries including an improvement on the error term in the Rankin-Selberg problem, and on certain subconvexity bounds for $GL_3 \times GL_2$ and $GL_3$ $L$-functions. As a byproduct of the method of proof, we also obtain an estimate for an average of shifted convolution sums of $GL_3$ Fourier coefficients.
- Subjects :
- Mathematics - Number Theory
11M41, 11F66
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2407.06962
- Document Type :
- Working Paper