Work

Surfaces Associated to Zeros of Automorphic $L$-functions

Year: 2026

Type: preprint

Abstract: Assuming the Riemann Hypothesis, Montgomery established results concerning pair correlation of zeros of the Riemann zeta function. Rudnick and Sarnak extended these results to automorphic $L$-functions and all level correlations. We discover additional geometric structures associated to the zeros of automorphic $L$-functions. In the case of pair correlation, these structures form certain surfaces which display Gaussian behavior. For triple correlation, these structures exhibit Laplace and Chi-squared distributions, revealing an unexpected phase transition.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.26575

Authors: Basak, Debmalya, Castillo, Cruz, Zaharescu, Alexandru

Institutions: University of Illinois Urbana-Champaign, IMAR - Institutul de Matematică „Simion Stoilow” al Academiei Române

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Alfred P. Sloan Foundation, Princeton University, University of Illinois at Urbana-Champaign

OpenAlex ID: W7223010804

Cites: 2

Cited by:

Related to: 10