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- W2804634405 abstract "Let $q in mathbb{Z} [i]$ be prime and $chi $ be the primitive quadratic Hecke character modulo $q$. Let $pi$ be a self-dual Hecke automorphic cusp form for $mathrm{SL}_3 (mathbb{Z} [i] )$ and $f$ be a Hecke cusp form for $Gamma_0 (q) subset mathrm{SL}_2 (mathbb{Z} [i])$. Consider the twisted $L$-functions $ L (s, pi otimes f otimes chi) $ and $L (s, pi otimes chi)$ on $mathrm{GL}_3 times mathrm{GL}_2$ and $mathrm{GL}_3$. We prove the subconvexity bounds begin{equation*} L big(tfrac 1 2, pi otimes f otimes chi big) ll_{, varepsilon, pi, f } mathrm{N} (q)^{5/4 + varepsilon}, L big(tfrac 1 2 + it, pi otimes chi big) ll_{, varepsilon, pi, t } mathrm{N} (q)^{5/8 + varepsilon}, end{equation*} for any $varepsilon > 0$." @default.
- W2804634405 created "2018-06-01" @default.
- W2804634405 creator A5050419826 @default.
- W2804634405 date "2018-05-15" @default.
- W2804634405 modified "2023-10-14" @default.
- W2804634405 title "Subconvexity for twisted $L$-functions on $mathrm{GL}_3$ over the Gaussian number field" @default.
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- W2804634405 doi "https://doi.org/10.48550/arxiv.1805.06026" @default.
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