Secondary terms in the distribution of genus numbers of cubic fields
Abstract
We prove the existence of secondary terms of order $X^{5/6}$ in the asymptotic formulas for the average size of the genus number of cubic fields and for the number of cubic fields with a given genus number, establishing improved error estimates. These results refine the estimates obtained by McGown and Tucker. We also provide uniform estimates for the moments of the genus numbers of cubic fields.
Fields of Study & Subjects
Analytic Number Theory Research
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 27 January 2026
- Document type
- Preprint