Bass Note Spectra of Binary Forms

Giorgos Kotsovolis

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arXiv · 2405.10252

Bass Note Spectra of Binary Forms

Giorgos Kotsovolis

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Abstract

We show that the spectrum of every $\mathbb{R}-$isotropic homogeneous binary form $P$ of degree $n\geq3$ is an interval of the form $[0,M_P],$ where $M_P$ is some positive constant. This completes the discussion around a conjecture of Mordell from 1940 (disproved by Davenport) regarding the existence of spectral gaps for binary cubic forms and further settles Mahler's program for binary forms of every degree.

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Giorgos Kotsovolis. 2024-05-16. Bass Note Spectra of Binary Forms. https://arxiv.org/abs/2405.10252

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