We describe a new method to obtain weak subconvexity bounds for -functions with mild hypotheses on the size of the Dirichlet coefficients. We verify these hypotheses for all automorphic -functions and (with mild restrictions) the Rankin–Selberg -functions attached to two automorphic representations. The proof relies on a new unconditional log-free zero density estimate for Rankin–Selberg -functions.
"Weak subconvexity without a Ramanujan hypothesis." Duke Math. J. 168 (7) 1231 - 1268, 15 May 2019. https://doi.org/10.1215/00127094-2018-0065