We show that the spectrum of every R-isotropic homogeneous binary form P of degree n≥3 is an interval of the form [0,MP], where MP 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) studied this question.
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