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On positive definite hermitian forms

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Abstract

Kneser's method of constructing adjacent lattices will be used to determine class numbers of unimodular positive definite hermitian lattices of rank 2 and 3 over rings of integers in some imaginary quadratic fields.

The same method will also be applied in order to construct indecomposable unimodular positive definite hermitian lattices of rank 2 and 3 over almost all orders in imaginary quadratic fields, even non-maximal ones. All exceptional cases will be determined explicitly.

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Authors and Affiliations

  1. Department of Mathematics Evans Hall, University of California, 94720, Berkeley, CA

    Detlev W. Hoffmann

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  1. Detlev W. Hoffmann
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Additional information

In part supported by NSF grant DMS 8805262. I would like to thank Prof. Martin Kneser for the support and the many helpful hints I received during the work on my Diplom thesis on which this paper is based, and also Prof. T.-Y. Lam for providing me with the grant without which I would not have been able to devote part of my time to writing this paper.

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Hoffmann, D.W. On positive definite hermitian forms. Manuscripta Math 71, 399–429 (1991). https://doi.org/10.1007/BF02568415

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