The least inert prime in a real quadratic field
نویسندگان
چکیده
منابع مشابه
The least inert prime in a real quadratic field
In this paper, we prove that for any positive fundamental discriminant D > 1596, there is always at least one prime p ≤ D0.45 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 √ D/2. We use a “smoothed” version of the Pólya–Vinogradov in...
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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 < p D=2 such that the Kronecker symbol (D=p) = ?1.
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(here b and a run over the quadratic nonresidues and quadratic residues, respectively, that lie between 0 and p) is a unit of the real quadratic field R(y/p), and that 77> 1. The fact that -n > 1 is usually deduced from the theory of the classnumber of quadratic fields. We present a short proof independent of the theory of the class-number. As in the paper of Chowla and Mordell [Note on the non...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2012
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2012-02579-8