Bass Note Spectra of Binary Forms

Abstract

We show that the spectrum of every $\mathbb{R}-$isotropic homogeneous binary form $P$ of degree $n\ge 3$ 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.

38 pages