The Burgess bound via a trivial delta method

2018/03/01 by Aggarwal, Keshav, Holowinsky, Roman, Lin, Yongxiao +1
#11F66 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1803.00542

Abstract

Let g be a fixed Hecke cusp form for SL(2,ℤ) and χ be a primitive Dirichlet character of conductor M. The best known subconvex bound for L(1/2,g⊗ χ) is of Burgess strength. The bound was proved by a couple of methods: shifted convolution sums and the Petersson/Kuznetsov formula analysis. It is natural to ask what inputs are really needed to prove a Burgess-type bound on \rm GL(2). In this paper, we give a new proof of the Burgess-type bounds L(1/2,g⊗ χ)≪_g,ε M^1/2-1/8+ε and L(1/2,χ)≪_ε M^1/4-1/16+ε that does not require the basic tools of the previous proofs and instead uses a trivial delta method.

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