The least inert prime in a real quadratic field
نویسنده
چکیده
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 inequality, which is very useful for numerically explicit estimates.
منابع مشابه
An Upper Bound on the Least Inert Prime in a Real Quadratic Field
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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ورودعنوان ژورنال:
- Math. Comput.
دوره 81 شماره
صفحات -
تاریخ انتشار 2012