Simple zeros of $L$-functions and the Weyl-type subconvexity

• Published in: Journal of the Korean Mathematical Society pp. 167 - 193
• Main Authors: 조재현, 오경원
• Format: Journal Article
• Language: English
• Published: 대한수학회 01-01-2023
• Subjects: 수학
• ISSN: 0304-9914; 2234-3008
• DOI: 10.4134/JKMS.j220242

Let $f$ be a self-dual primitive Maass or modular forms for level $4$. For such a form $f$, we define \begin{align*} N_f^s(T)\!:=\!|\{\rho \in \mathbb{C} : |\Im(\rho)| \leq T, \text{ $\rho$ is a non-trivial simple zero of $L_f(s)$} \}|. \end{align*} We establish an omega result for $N_f^s(T)$, which is $N_f^s(T)=\Omega \big( T^{\frac{1}{6}-\epsilon} \big)$ for any $\epsilon>0$. For this purpose, we need to establish the Weyl-type subconvexity for $L$-functions attached to primitive Maass forms by following a recent work of Aggarwal, Holowinsky, Lin, and Qi. KCI Citation Count: 0