Year: 2024
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Kotsovolis, Giorgos
Institution: Princeton University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4397028796