The representation of binary quadratic forms by positive definite quaternary quadratic forms

Earnest, A. G.

doi:10.1090/S0002-9947-1994-1264145-0

The representation of binary quadratic forms by positive definite quaternary quadratic forms
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by A. G. Earnest PDF

Trans. Amer. Math. Soc. 345 (1994), 853-863 Request permission

Abstract:

A quadratic $\mathbb {Z}$-lattice L of rank n is denned to be k-regular for a positive integer $k \leq n$ if L globally represents all quadratic $\mathbb {Z}$-lattices of rank k which are represented everywhere locally by L. It is shown that there exist only finitely many isometry classes of primitive positive definite quadratic $\mathbb {Z}$-lattices of rank 4 which are 2-regular.

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