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On extreme values of quadratic twists of Dirichlet-type $L$-functions
- Publication Year :
- 2024
-
Abstract
- In a recent work arXiv:2004.14450, it has been shown that $L$-functions associated with arbitrary non-zero cusp forms take large values at the central critical point. The goal of this note is to derive analogous results for twists of Dirichlet-type functions. More precisely, for an odd integer $q >1$, let $F$ be a non-zero $\mathbb{C}$-linear combination of primitive, complex, even Dirichlet characters of conductor $q$. We show that for any $\epsilon>0$ and sufficiently large $X$, there are $\gg X^{1-\epsilon}$ fundamental discriminants $8d$ with $X < d \leq 2X$ and ${(d, 2q)=1}$ such that ${|L(1/2, F \otimes \chi_{8d})| }$ is large.
- Subjects :
- Mathematics - Number Theory
11M06
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2405.02443
- Document Type :
- Working Paper