Class numbers of binary quadratic polynomials

Zichen Yang

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arXiv · 2409.06244

Class numbers of binary quadratic polynomials

Zichen Yang

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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.

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Zichen Yang. 2024-09-10. Class numbers of binary quadratic polynomials. https://arxiv.org/abs/2409.06244

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