Class numbers of binary quadratic polynomials
Number Theory
2025-01-29 v2
Abstract
In this paper, we give a formula for the proper class number of a binary quadratic polynomial assuming that the conductor ideal is sufficiently divisible at dyadic places. This allows us to study the growth of the proper class numbers of totally positive binary quadratic polynomials. As an application, we prove finiteness results on totally positive binary quadratic polynomials with a fixed quadratic part and a fixed proper class number.
Cite
@article{arxiv.2409.06244,
title = {Class numbers of binary quadratic polynomials},
author = {Zichen Yang},
journal= {arXiv preprint arXiv:2409.06244},
year = {2025}
}
Comments
15 pages