Weak subconvexity without a Ramanujan hypothesis

Abstract

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.

25 pages. Appendix by Farrell Brumley. Referee comments incorporated

References in corpus (3)

• Standard Zero-Free Regions for Rankin--Selberg L-Functions via Sieve Theory
• Convexity bounds for L-functions
• On sums of Hecke-Maass eigenvalues squared over primes in short intervals

Cited by in corpus (14)

• Effective forms of the Sato--Tate conjecture
• A zero density estimate for Dedekind zeta functions
• A Bombieri-Vinogradov theorem for higher rank groups
• An unconditional $\mathrm{GL}(n)$ large sieve
• Towards a ${\mathrm{GL}}_n$ variant of the Hoheisel phenomenon
• An approximate form of Artin's holomorphy conjecture and non-vanishing of Artin $L$-functions
• Zeros of Rankin-Selberg $L$-functions in families
• A new zero-free region for Rankin-Selberg $L$-functions
• Effective decorrelation of Hecke eigenforms
• Patterns of primes in the Sato-Tate conjecture
• Highly Uniform Prime Number Theorems
• New variants of arithmetic quantum ergodicity
• Effective quantum unique ergodicity for Hecke-Maass newforms and Landau-Siegel zeros
• Exceptional zeros of Rankin-Selberg $L$-functions and joint Sato-Tate distributions