Binary forms with covariant points close to the real axis

2024/09/21 by Eugenia Rosu, Rosu, Eugenia
Mathematics · #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2409.14112

openalex publication_date 2024/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a real binary form F(X, Z), Stoll and Cremona have defined a reduction theory using the action of the modular group SL₂(ℤ), and associated to each binary form a covariant point z(F) located in the upper half plane. When the point z(F) is close to the real axis, then at least half of the roots will be on a circle of small radius r. Conversely, we find conditions depending on the radius r such that the covariant point z(F) to be close to the real axis. The results have further applications to improving the reduction algorithm for binary forms of Stoll and Cremona.

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