Relative Trace Formula and Twisted L-functions: the Burgess Bound

2023/05/18 by Yang, Liyang
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2305.10719

Abstract

Let F be a number field, π either a unitary cuspidal automorphic representation of GL(2)/F or a unitary Eisenstein series, and χ a unitary Hecke character of analytic conductor C(χ). We develop a regularized relative trace formula to prove a refined hybrid subconvex bound for L(1/2,π×χ). In particular, we obtain the Burgess subconvex bound L(1/2,π×χ)≪_π,F,εC(χ)^{(1)/(2)-(1)/(8)+ε}, where the implied constant depends on π, F and ε.

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