On the growth of Rankin-Selberg L-functions for $SL(2)$

Hongyu He

On the growth of Rankin-Selberg L-functions for $SL(2)$

Representation Theory 2020-08-28 v1 Number Theory

Authors: Hongyu He

Abstract

In this paper, we establish bounds of the Rankin-Selberg $L$ -function for $SL(2)$ using the supnorm of the Eisenstein series and a purely representation theoretic index over the real group. Consequently, we obtain a subconvexity bound $L(\frac{1}{2}+ it, f_1 \times f_2) \leq C (1+ |t|)^{\frac{5}{6}+\epsilon}$ for two Maass cusp forms of $SL(2, \mathbb Z)$ .

Keywords

Rankin-Selberg L-function SL(2) Eisenstein series subconvexity bound Maass cusp forms

Cite

@article{arxiv.2008.11771,
  title  = {On the growth of Rankin-Selberg L-functions for $SL(2)$},
  author = {Hongyu He},
  journal= {arXiv preprint arXiv:2008.11771},
  year   = {2020}
}

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