The least inert prime in a real quadratic field
Author:
Enrique Treviño
Journal:
Math. Comp. 81 (2012), 1777-1797
MSC (2010):
Primary 11L40, 11Y40, 11R11
DOI:
https://doi.org/10.1090/S0025-5718-2012-02579-8
Published electronically:
February 10, 2012
MathSciNet review:
2904602
Full-text PDF
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Abstract: In this paper, we prove that for any positive fundamental discriminant , there is always at least one prime
such that the Kronecker symbol
. This improves a result of Granville, Mollin and Williams, where they showed that the least inert prime
in a real quadratic field of discriminant
is at most
. We use a ``smoothed'' version of the Pólya-Vinogradov inequality, which is very useful for numerically explicit estimates.
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Additional Information
Enrique Treviño
Affiliation:
Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755
Address at time of publication:
Department of Mathematics and Statistics, Swarthmore College, Swarthmore, Pennsylvania 19081
Email:
etrevin1@swarthmore.edu
DOI:
https://doi.org/10.1090/S0025-5718-2012-02579-8
Keywords:
Character Sums,
Pólya–Vinogradov inequality,
quadratic fields
Received by editor(s):
May 10, 2011
Received by editor(s) in revised form:
June 8, 2011
Published electronically:
February 10, 2012
Additional Notes:
This paper is essentially Chapter 3 of the author’s Ph.D. Dissertation [16].
Article copyright:
© Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.