First Moment of Quadratic Hecke L-Functions with Lower Order Term

2025/12/27 by Peng Gao, Liangyi Zhao, Gao, Peng +1
Mathematics · #11M06 #11M41 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2512.22509

openalex publication_date 2025/12/27 · openalex created_date 2025/12/31 · openalex updated_date 2026/07/28

Abstract

We evaluate the first moment of the family of primitive quadratic Hecke L-functions in the Gaussian field using the method of double Dirichlet series under the Riemann hypothesis and the Lindelöf hypothesis. We obtain asymptotic formulas with secondary main terms and error terms of size that is one quarter of that of the main term.

Citations

• First moment of quadratic Dirichlet L-functions with secondary terms
• The Ratios conjecture for real Dirichlet characters and multiple Dirichlet series
• L-functions with n-th order twists

Related

• First moment of quadratic Dirichlet L-functions with secondary terms
• First moment of central values of Hecke L-functions with Fixed Order Characters
• The fourth moment of central values of quadratic Hecke L-functions in\n the Gaussian field
• Moments and Non-vanishing of central values of Quadratic Hecke L-functions in the Gaussian Field
• First moment of central values of quadratic Dirichlet L-functions