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Uniform subconvex bounds for Rankin-Selberg L-functions · arXivDesk

2110.08682Oct 16, 202128 pages. Comments are welcome! arXiv admin note: substantial text overlap with arXiv:2108.09410

Uniform subconvex bounds for Rankin-Selberg $L$ -functions

Qingfeng Sun

Abstract

Let $f$ be a Maass cusp form for $\rm SL_2(\mathbb{Z})$ with Laplace eigenvalue $1/4+μ_f^2$

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Let f be a Maass cusp form for SL₂(Z) with Laplace eigenvalue 1/4+μ_f², μ_f>0. Let g be an arbitrary but fixed holomorphic or Maass cusp form for SL₂(Z).

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Claims

The paper addresses: Uniform subconvex bounds for Rankin-Selberg L-functions.
Let f be a Maass cusp form for SL₂(Z) with Laplace eigenvalue 1/4+μ_f², μ_f>0.

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Author comment: 28 pages. Comments are welcome! arXiv admin note: substantial text overlap with arXiv:2108.09410

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Nearby in the stack

,

μ_f>0

. Let

g

be an arbitrary but fixed holomorphic or Maass cusp form for

\rm SL_2(\mathbb{Z})

. In this paper, we establish the following uniform subconvexity bound for the Rankin-Selberg

L

-function

L(s,f\otimes g)

L\left(1/2+it,f\otimes g\right)\ll (μ_f+|t|)^{9/10+\varepsilon},

where the implied constant depends only on

\varepsilon

and

g

.

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