Large values of Dirichlet L- functions inside the critical strip

2018/03/10 by Marc Munsch, Munsch, Marc
Mathematics · #11M06 #11R11 #11R29 #11R42 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1803.03836

openalex publication_date 2018/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper, we study large values of Dirichlet L- functions inside the critical strip. For every 1/20 such that log \vert L(σ,χ)\vert ≫ c(σ)(log q)^1-σ(loglog q)^-σ. This matches the believed prediction for these values which was previously known only for the Riemann zeta function since Montgomery, or conditionally on GRH for quadratic L- functions due to Lamzouri. In a recent work involving the author, a new implementation of the resonance method was presented in order to exhibit large values of the Riemann zeta function on the line \Re(s)=1. We show how to adapt the argument to our setting.

Citations

• Integral moments of L-functions

Related

• Extreme values of the Dirichlet L-functions at the critical points of the Riemann zeta function
• On large values of L(σ,χ)
• Large values of quadratic Dirichlet L-functions
• Estimates for L-functions in the critical strip under GRH with effective applications
• Simultaneous large values and dependence of Dirichlet L-functions in the critical strip