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An algebraic approach to the growth of class numbers of binary quadratic lattices

Published online by Cambridge University Press:  26 February 2010

A. G. Earnest  and
Dennis R. Estes
A. G. Earnest
Affiliation:
Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901, U.S.A.
Dennis R. Estes
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, California 90007, U.S.A.
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Two basic approaches have been used to develop explicit formulae for the number of classes in a genus of binary quadratic lattices over an algebraic number field. Analytic machinery in the form of the Minkowski-Siegel Mass Formula or the Tamagawa number of an algebraic group was employed by Pfeuffer [13] and Shyr [17] to obtain such a formula for maximal positive definite lattices over totally real number fields. On the other hand, Peters [10] observed that a formula applicable to maximal lattices over any number field can be deduced by algebraic methods from the theory of quadratic field extensions. Using group-theoretic techniques set up by the present authors [3] along with the calculation of certain local unit indices, Korner [6] derived the corresponding formula for non-maximal lattices.

Type
Research Article
Information
Mathematika , Volume 28 , Issue 2 , December 1981 , pp. 160 - 168
Copyright
Copyright © University College London 1981

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