On elements of prescribed norm in maximal orders of a quaternion algebra
Canadian journal of mathematics, Tome 77 (2025) no. 6, pp. 1938-1965
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Let $\mathcal {O}$ be a maximal order in the quaternion algebra over $\mathbb Q$ ramified at p and $\infty $. We prove two theorems that allow us to recover the structure of $\mathcal {O}$ from limited information. The first says that for any infinite set S of integers coprime to p, $\mathcal {O}$ is spanned as a ${\mathbb {Z}}$-module by elements with norm in S. The second says that $\mathcal {O}$ is determined up to isomorphism by its theta function.
Mots-clés :
Quaternion algebra, maximal order, theta function, quadratic form, norm
Goren, Eyal Z.; Love, Jonathan R. On elements of prescribed norm in maximal orders of a quaternion algebra. Canadian journal of mathematics, Tome 77 (2025) no. 6, pp. 1938-1965. doi: 10.4153/S0008414X24000592
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author = {Goren, Eyal Z. and Love, Jonathan R.},
title = {On elements of prescribed norm in maximal orders of a quaternion algebra},
journal = {Canadian journal of mathematics},
pages = {1938--1965},
year = {2025},
volume = {77},
number = {6},
doi = {10.4153/S0008414X24000592},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X24000592/}
}
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