Hybrid Bounds on Twisted L-Functions Associated to Modular Forms

2013/11/07 by Kuan, Chan Ieong
#11F11 #11F12 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1311.1826

Abstract

For f a primitive holomorphic cusp form of even weight k ≥ 4, level N, and χ a Dirichlet character mod Q with (Q,N)=1, we establish a new hybrid subconvexity bound for L(1/2 + it, f_χ), which improves upon all known hybrid bounds. This is done via amplification and taking advantage of a shifted convolution sum of two variables defined and analyzed in a recent paper of Hoffstein and Hulse.

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