Extreme values of zeta and L-functions

2007/08/29 by K. Soundararajan, Soundararajan, K. · 8 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0708.3990

openalex publication_date 2007/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a "resonance" method to produce large values of |ζ(1/2+it)| and large and small central values of L-functions.

Citations

• Nonvanishing of Quadratic Dirichlet L-Functions at S = &#189

Cited by

• Extreme values of quadratic Dirichlet L-functions with prime-related moduli
• Large values of derivatives of the Riemann zeta function on vertical homogeneous progressions
• Explicit extreme values of the argument of the Riemann zeta-function
• The mollified fourth moment of Dirichlet L-functions
• Decorrelation of SO(5)× SO(2) Bessel periods for symmetric cubes of GL(2)
• Large values of quadratic Dirichlet L-functions near the central point
• Selberg orthogonality for half-integral weight modular forms
• Extreme values of derivatives of the Dedekind zeta function of a cyclotomic field

Related

• Simultaneous extreme values of zeta and L-functions
• Large values of Dirichlet L- functions inside the critical strip
• Extreme values of |ζ(1+it)|
• On large values of L(σ,χ)
• Extreme values of the Riemann zeta function on the 1-line