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

Andrew Granville, R. A. Mollin, Hywel C Williams

Type: Article

Publication Date: 2000-04-01

Citations: 10

DOI: https://doi.org/10.4153/cjm-2000-017-5

Abstract

Abstract 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 < √ D /2 such that the Kronecker symbol ( D/p ) = −1.

Locations

Canadian Journal of Mathematics - View - PDF

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Works Cited by This (9)

Action	Title	Year	Authors
+ PDF Chat	Approximate formulas for some functions of prime numbers	1962	J. Barkley Rosser Lowell Schoenfeld
+	Multiplicative Number Theory	1980	H. Davenport
+	On Character Sums and <i>L</i> -Series. II	1963	D. A. Burgess
+ PDF Chat	Explicit bounds for primality testing and related problems	1990	Eric Bach
+ PDF Chat	Some results on pseudosquares	1996	Richard Lukes C. Patterson Hywel C Williams
+	Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x)	1975	J. Barkley Rosser Lowell Schoenfeld
+	Bounds for sequences of consecutive power residues. I	1973	Karl K. Norton
+	On Character Sums and L-Series<sup>†</sup>	1962	D. A. Burgess
+	Tables of indices and primitive roots	1968	A. E. Western J. C. P. Miller