Subconvexity for Twisted L-Functions on GL(3)×GL(2) and GL(3)

Abstract

Let φ be the symmetric-square lift of an SL2(Z) Hecke-Maass form. Let q be an odd cube-free positive integer, and let χ be a primitive Dirichlet character modulo q such that χ is not quadratic. Let f be an even Hecke-normalized Hecke-Maass newform of level dividing q, central character χ2, and spectral parameter tf . In this thesis, we show the following subconvexity bounds for twisted L-functions on GL(3) × GL(2) and GL(3): L (1 2, φ × f × χ ) φ,tf , q 5 4 + , L (1 2 + it, φ × χ ) φ,t, q 5 8 + , (1) for every > 0, where the dependence of the implied constants on tf , t are polynomial.