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Class numbers of quadratic forms over real quadratic fields

Published online by Cambridge University Press:  22 January 2016

Yoshiyuki Kitaoka
Yoshiyuki Kitaoka*
Affiliation:
Nagoya University
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Let k be an algebraic number field, let K be a Galois extension of k of finite degree, and let OK, Ok be the maximal orders of K, k, respectively. We consider the conjugate operation: for a given quadratic lattice M over OK equipped with a bilinear form B and for an automorphism σ ∈ G(K/k), we define a new quadratic lattice Mσ over OK. Here Mσ has the same underlying abelian group as M, but a new OK-action ; the new bilinear form Bσ on Mσ is defined by

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 66 , May 1977 , pp. 89 - 98
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1977

References

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