Bass Note Spectra of Binary Forms
Giorgos Kotsovolis

TL;DR
This paper proves that the spectrum of any real isotropic homogeneous binary form of degree three or higher is a continuous interval from zero to a positive maximum, resolving longstanding conjectures in the field.
Contribution
It establishes that the spectrum of such binary forms is always an interval, confirming a conjecture related to spectral gaps and completing Mahler's program for all degrees.
Findings
Spectrum of binary forms is an interval [0, M_P]
Resolves Mordell's conjecture from 1940
Completes Mahler's program for binary forms
Abstract
We show that the spectrum of every isotropic homogeneous binary form of degree is an interval of the form where 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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Taxonomy
TopicsMusic Technology and Sound Studies
