Year: 2026
Type: preprint
Abstract: We show that for a fixed $\mathrm{SL}_3(\mathbb Z)$ Hecke--Maass cusp form $F$, there are infinitely many primitive Dirichlet characters $χ$ such that $L(1/2, F\times χ)$ and $L(1/2, χ)$ do not vanish \emph{simultaneously}. More precisely, we obtain an asympotic formula with a {\em power-saving} error term for the product of these central values averaged over $\{χ\bmod q: q\in \mathcal Q\}$ where $\mathcal Q$ is a set of squarefree integers with a small divisor of suitable size.
Source: arXiv (Cornell University)
Authors: Li, Junxian, Li, Xiannan, Lin, Yongxiao
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221098519