Bounds on discriminants with one class per genus

2004/01/23 by Kimberly Hopkins, Hopkins, Kimberly
Mathematics · #11M26 #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.NT #msc:11M26

paper · pdf · doi:10.48550/arxiv.math/0401334

Name change (original name: Spears)

openalex publication_date 2004/01/23 · arxiv created 2009/07/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We assume a condition on the zeros of Dirichlet L-functions related to the GUE distribution to show there are no discriminants greater than d₆₆≈ 1.9 x 10¹³⁰ with one class per genus.

Related

• Bounds on the largest prime factor of a negative discriminant with one class per genus
• Large values of quadratic Dirichlet L-functions
• Spacing of zeros of Hecke L-functions and the class number problem
• Function Fields of Class Number One
• Dirichlet's Lemma in Number Fields