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- W1668908051 abstract "A rational positive-definite quadratic form is perfect if it can be reconstructed from the knowledge of its minimal nonzero value m and the finite set of integral vectors v such that f(v) = m. This concept was introduced by Voronoi and later generalized by Koecher to arbitrary number fields. One knows that up to a natural change of variables'' equivalence, there are only finitely many perfect forms, and given an initial perfect form one knows how to explicitly compute all perfect forms up to equivalence. In this paper we investigate perfect forms over totally real number fields. Our main result explains how to find an initial perfect form for any such field. We also compute the inequivalent binary perfect forms over real quadratic fields Q(sqrt{d}) with d leq 66." @default.
- W1668908051 created "2016-06-24" @default.
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- W1668908051 date "2009-08-21" @default.
- W1668908051 modified "2023-09-27" @default.
- W1668908051 title "Perfect forms over totally real number fields" @default.
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