On realization of isometries for higher rank quadratic lattices over number fields

Chan, Wai Kiu; Li, Han

doi:10.1090/tran/8670

On realization of isometries for higher rank quadratic lattices over number fields
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by Wai Kiu Chan and Han Li PDF

Trans. Amer. Math. Soc. 375 (2022), 4619-4640 Request permission

Abstract:

Let $F$ be a number field, and $n\geq 3$ be an integer. In this paper we give an effective procedure which (1) determines whether two given quadratic lattices on $F^n$ are isometric or not, and (2) produces an invertible linear transformation realizing the isometry provided the two given lattices are isometric. A key ingredient in our approach is a search bound for the equivalence of two given quadratic forms over number fields which we prove using methods from algebraic groups, homogeneous dynamics and spectral theory of automorphic forms.

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