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Minimal discriminants of indefinite ternary quadratic forms having specified class number

Published online by Cambridge University Press:  26 February 2010

A. G Earnest
A. G Earnest
Affiliation:
Department of Mathematics, Southern Illinois UniversityCarbondale, Illinois, USA. 62901-4408
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In order for an indefinite integral ternary quadratic form to have class number exceeding one, its discriminant must be divisible by the cube of at least one odd prime, or by a sufficiently large power of 2 (see [4], [1]). More generally, for such a form to have class number 2t, t> 1, it is necessary not only that the discriminant be divisible by at least t distinct primes, but also that these primes interact with each other in rather specific ways. Consequently, the minimal absolute value ∆(t) of the discriminant of an indefinite integral ternary quadratic form of class number 2' increases rapidly as a function of the natural number t.

Type
Research Article
Information
Mathematika , Volume 35 , Issue 1 , June 1988 , pp. 95 - 100
Copyright
Copyright © University College London 1988

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References

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