Paper Info
Title
The least inert prime in a real quadratic field.
Abstract
In this paper, we prove that for any positive fundamental discriminant D > 1596, there is always at least one prime p <= D-0.45 such that the Kronecker symbol (D/p)= -1. This improves a result of Granville, Mollin and Williams, where they showed that the least inert prime p in a real quadratic field of discriminant D > 3705 is at most root D/2. We use a "smoothed" version of the Polya-Vinogradov inequality, which is very useful for numerically explicit estimates.
Year
DOI
Venue
2012
10.1090/S0025-5718-2012-02579-8
MATHEMATICS OF COMPUTATION
Keywords
DocType
Volume
Character Sums,Polya-Vinogradov inequality,quadratic fields
Journal
81
Issue
ISSN
Citations 
279
0025-5718
0
PageRank 
References 
Authors
0.34
3
1
Name
Order
Citations
PageRank
Enrique Treviño100.34