Work

Log-correlation for shifted Dirichlet 𝐿-functions and Dedekind zeta functions of quadratic fields

Year: 2025

Type: article

Abstract: Adapting a method of Radziwiłł and Soundararajan, we prove a generalisation of Bourgade’s central limit theorem (on shifted Riemann zeta functions) for Dirichlet 𝐿-functions and Dedekind zeta functions of quadratic fields. As an application, we obtain logarithmic correlation results for shifted Dirichlet 𝐿-functions and shifted Dedekind zeta functions. These are inspired by two assumptions regarding the joint value distribution of two given shifted Riemann zeta functions, considered by Harper in le séminaire Nicolas Bourbaki.

Source: Forum Mathematicum

DOI: 10.1515/forum-2023-0224

Authors: Po-Han Hsu, Peng-Jie Wong

Institution: National Sun Yat-sen University

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,712

Funder: National Science and Technology Council