The maximum size of L-functions

2005/06/11 by David W. Farmer, Farmer, David W., S. M. Gonek +3 · 4 citations
Computer Science · Mathematics · #11M26 #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.math/0506218

openalex publication_date 2005/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We conjecture the true rate of growth of the maximum size of the Riemann zeta function and other L-functions. We support our conjecture using arguments from random matrix theory, conjectures for moments of L-functions, and also by assuming a random model for the primes.

Citations

• Integral moments of L-functions
• Mean values of L-functions and symmetry

Cited by

• Extreme values of quadratic Dirichlet L-functions with prime-related moduli
• Upper bounds on gaps between zeros of L-functions
• Extreme values of class group L-functions
• Large values of quadratic Dirichlet L-functions near the central point

Related

• A note on the maximum of the Riemann zeta function, and log-correlated random variables
• The Riemann zeta function in short intervals [after Najnudel, and Arguin, Belius, Bourgade, Radziwiłł, and Soundararajan]
• Upper bounds on L-functions at the edge of the critical strip
• L-functions and random matrices
• On large gaps between zeros of L-functions from branches