Subconvexity bounds for $\textrm{GL(3)}\times \textrm{GL(2)}$ $L$-functions in $\textrm{GL(2)}$ spectral aspect

Sumit Kumar

doi:10.4171/jems/1383

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Subconvexity bounds for $GL(3) \times GL(2)$ $L$ -functions in $GL(2)$ spectral aspect

Sumit Kumar
Alfréd Rényi Institute of Mathematics,Budapest 1053, Hungary

$Subconvexity bounds for $\textrm{GL(3)}\times \textrm{GL(2)}$ $L$-functions in $\textrm{GL(2)}$ spectral aspect cover$

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Abstract

Let $π$ be a Hecke–Maass cusp form for $SL (3, Z)$ and $f$ be a holomorphic cusp form for $SL (2, Z)$ of weight $k$ or a Hecke–Maass cusp form corresponding to the Laplacian eigenvalue $1/4 + k^{2}$ , $k \geq 1$ , for $SL (2, Z)$ . In this paper, we prove the following subconvexity bound:

L (1/2, π \times f) ≪_{π, ε} k^{3/2 - 1/51 + ε} .

Cite this article

Sumit Kumar, Subconvexity bounds for $GL(3) \times GL(2)$ $L$ -functions in $GL(2)$ spectral aspect. J. Eur. Math. Soc. (2023), published online first

DOI 10.4171/JEMS/1383