Isomorphic Invariant Orders Without Hermite Equivalence
Year: 2026
Type: article
Abstract: Bhargava, Evertse, Győry, Remete and Swaminathan asked whether, in every degree n ≥ 4, there are integral polynomials with isomorphic invariant orders that are not Hermite equivalent; they answered the question for n = 4. This paper answers it for every even n and for every n with n − 2 divisible by 3, 5 or 7, with explicit pairs. In degree six one polynomial of the pair can be chosen monic. LaTeX source, figures, PDF and a verification script.
Author: Bhattacharjee, Deep
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225770167
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