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UNIFORM BOUNDS FOR
$\operatorname {GL}(3)\times \operatorname {GL}(2)$ L-FUNCTIONS
Published online by Cambridge University Press: 17 October 2023
Abstract
In this paper, we prove uniform bounds for $\operatorname {GL}(3)\times \operatorname {GL}(2) \ L$-functions in the
$\operatorname {GL}(2)$ spectral aspect and the t aspect by a delta method. More precisely, let
$\phi $ be a Hecke–Maass cusp form for
$\operatorname {SL}(3,\mathbb {Z})$ and f a Hecke–Maass cusp form for
$\operatorname {SL}(2,\mathbb {Z})$ with the spectral parameter
$t_f$. Then for
$t\in \mathbb {R}$ and any
$\varepsilon>0$, we have
$$\begin{align*}L(1/2+it,\phi\times f) \ll_{\phi,\varepsilon} (t_f+|t|)^{27/20+\varepsilon}. \end{align*}$$
$L(1/2+it,\phi \times f)$ whenever
$|t|-t_f \gg (|t|+t_f)^{3/5+\varepsilon }$.
- Type
- Research Article
- Information
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press
References
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