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An Upper Bound on the Least Inert Prime in a Real Quadratic Field

Published online by Cambridge University Press:  20 November 2018

Andrew Granville ,
R. A. Mollin  and
H. C. Williams
Andrew Granville
Affiliation:
Department of Mathematics, University of Georgia, Athens, GA 30602, USA email: andrew@math.uga.edu
R. A. Mollin
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, AB, T2N 1N4 email: ramollin@math.ucalgary.ca
H. C. Williams
Affiliation:
Department of Computer Science, University of Manitoba, Winnipeg, Manitoba, R3T 2N2 email: williams@cs.umanitoba.ca
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Abstract

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It is shown by a combination of analytic and computational techniques that for any positive fundamental discriminant $D\,>\,3705$, there is always at least one prime $p\,<\,\sqrt{D}/2$ such that the Kronecker symbol $(D/P)\,=\,-1$.

Keywords

11Y1111Y40
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 52 , Issue 2 , 01 April 2000 , pp. 369 - 380
Copyright
Copyright © Canadian Mathematical Society 2000

References

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