Hybrid subconvexity bounds for twists of $\mathrm{GL}(3)\times \mathrm{GL}(2)$ $L$-functions

Abstract

In this paper, we solve the hybrid subconvexity problem for $\mathrm{GL}(3)\times \mathrm{GL}(2)$ $L$-functions twisted by a primtive Dirichlet charater modulo $M$ (prime) in the $M$- and $t$-aspects. We also improve hybrid subconvexity bounds for twists of $\mathrm{GL}(3)$ $L$-functions in the $M$- and $t$-aspects.

arXiv comment36 pages. Incorporate the referee's comments and corrections. Comments welcome!

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• The subconvexity problem for $\GL_{2}$
• Distribution of mass of holomorphic cusp forms
• On the Rankin--Selberg problem
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• Oscillatory integrals with uniformity in parameters
• Analytic twists of $\mathrm{G}{\mathrm{L}}_3\times \mathrm{G}{\mathrm{L}}_2$ automorphic forms
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Cited by in corpus (1)

• Strong Hybrid Subconvexity for Twisted Selfdual ${\mathrm{GL}}_3$ $L$-Functions