Weak subconvexity without a Ramanujan hypothesis

By Kannan Soundararajan, Jesse Thorner. Duke mathematical journal, 2018

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We describe a new method to obtain weak subconvexity bounds for $L$-functions with mild hypotheses on the size of the Dirichlet coefficients. We verify these hypotheses for all automorphic $L$-functions and (with mild restrictions) the Rankin-Selberg $L$-functions attached to two automorphic representations. The proof relies on a new unconditional log-free zero density estimate for Rankin-Selberg $L$-functions.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8faaae37ba7337b950de141bd3efc952a31ec146