The Weyl bound for triple product L-functions

Abstract

Let ${\pi }_1,{\pi }_2,{\pi }_3$ be three cuspidal automorphic representations for the group $\mathrm{SL}(2,\mathbb{Z})$, where ${\pi }_1$ and ${\pi }_2$ are fixed and ${\pi }_3$ has large conductor. We prove a subconvex bound for $L(1/2,{\pi }_1\otimes {\pi }_2\otimes {\pi }_3)$ of Weyl-type quality. Allowing ${\pi }_3$ to be an Eisenstein series we also obtain a Weyl-type subconvex bound for $L(1/2+it,{\pi }_1\otimes {\pi }_2)$.

arXiv commentminor updates; to appear in Duke Math. J

References in corpus (14)

• The subconvexity problem for $\GL_{2}$
• Distribution of mass of holomorphic cusp forms
• The second moment of twisted modular L-functions
• The Weyl bound for Dirichlet $L$-functions of cube-free conductor
• The fourth moment of Dirichlet $L$-functions along a coset and the Weyl bound
• Real zeros of holomorphic Hecke cusp forms
• Oscillatory integrals with uniformity in parameters
• Rankin Triple Products and Quantum Chaos
• Standard Zero-Free Regions for Rankin--Selberg L-Functions via Sieve Theory
• Sub-Weyl subconvexity for Dirichlet L-functions to prime power moduli
• Subconvex equidistribution of cusp forms: reduction to Eisenstein observables
• Eisenstein series and the cubic moment for PGL(2)
• $t$-aspect subconvexity for $GL(2)\times GL(2)$ $L$-function
• Analytic newvectors for ${\mathrm{GL}}_n(\mathbb{R})$

Cited by in corpus (4)

• Local integral transforms and global spectral decomposition
• Uniform subconvex bounds for Rankin-Selberg $L$-functions
• Dissipation of correlations of holomorphic cusp forms
• Hybrid Weyl-type bound for $p$-power twisted $\mathrm{GL}(2)$ $L$-functions