Bounds for twists of GL(3) LL-functions

  • Yongxiao Lin

    The Ohio State University, Columbus, USA
Bounds for twists of GL(3) $L$-functions cover
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Let π\pi be a fixed Hecke–Maass cusp form for SL(3,Z)\mathrm{SL}(3,\mathbb{Z}) and χ\chi be a primitive Dirichlet character modulo MM, which we assume to be a prime. Let L(s,πχ)L(s,\pi\otimes \chi) be the LL-function associated to πχ\pi\otimes \chi. For any given ε>0\varepsilon > 0, we establish a subconvex bound L(1/2+it,πχ)π,ε(M(t+1))3/41/36+εL(1/2+it, \pi\otimes \chi)\ll_{\pi, \varepsilon} (M(|t|+1))^{3/4-1/36+\varepsilon}, uniformly in both the MM- and tt-aspects.

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Yongxiao Lin, Bounds for twists of GL(3) LL-functions. J. Eur. Math. Soc. 23 (2021), no. 6, pp. 1899–1924

DOI 10.4171/JEMS/1046