Year: 2026
Type: preprint
Abstract: We prove zero density estimates for $L$-functions of cuspidal automorphic representations $π$ of $\mathrm{GL}_2(\mathbb{A}_{\mathbb{Q}})$. We show that $N_π(σ, T) \ll T^{\frac{5}{2}(1 - σ) + o(1)}$, where $N_π(σ, T)$ denotes the number of zeros $ρ= β+ iγ$ of $L(s,π)$ with $β\geq σ$ and $|γ| \leq T$. The key input is an extension of the Guth$\unicode{x2013}$Maynard argument to Dirichlet polynomials whose coefficients satisfy a weaker $\ell^q$ bound.
Source: arXiv (Cornell University)
Author: Cossaboom, Catherine
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214226077