## Nearly unimodular quadratic forms.(English)Zbl 0842.11012

A $$\mathbb Z$$-lattice $$L$$ is called nearly unimodular if it has a Gram matrix of the form $\left( \begin{smallmatrix} a_1 &1 \\ 1 &a_2 & \ddots\\ & \ddots &\ddots \\ &&&a_{n-1} &1\\ &&&1 &a_n \end{smallmatrix} \right)=: [a_1, \dots, a_n ]=: A$ (then we denote $$L\cong A)$$. The main result is the following classification theorem: Let $$A= [a_1, \dots, a_n ]$$ and $$B= [b_1, \dots, b_n ]$$. Suppose $$L$$ and $$M$$ are positive definite nearly unimodular $$\mathbb Z$$-lattices with $$L\cong A$$ and $$M\cong B$$. Then $$L$$ is isometric to $$M$$ if and only if $$B= A$$ or $$B= [a_n, \dots, a_1]$$.

### MSC:

 1.1e+13 Quadratic forms over global rings and fields
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