An Upper Bound on the Least Inert Prime in a Real Quadratic Field
Canadian journal of mathematics, Tome 52 (2000) no. 2, pp. 369-380

Voir la notice de l'article provenant de la source Cambridge University Press

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 $p\,<\,\sqrt{D}/2$ such that the Kronecker symbol $(D/P)\,=\,-1$ .
DOI : 10.4153/CJM-2000-017-5
Mots-clés : 11Y11, 11Y40
Granville, Andrew; Mollin, R. A.; Williams, H. C. An Upper Bound on the Least Inert Prime in a Real Quadratic Field. Canadian journal of mathematics, Tome 52 (2000) no. 2, pp. 369-380. doi: 10.4153/CJM-2000-017-5
@article{10_4153_CJM_2000_017_5,
     author = {Granville, Andrew and Mollin, R. A. and Williams, H. C.},
     title = {An {Upper} {Bound} on the {Least} {Inert} {Prime} in a {Real} {Quadratic} {Field}},
     journal = {Canadian journal of mathematics},
     pages = {369--380},
     year = {2000},
     volume = {52},
     number = {2},
     doi = {10.4153/CJM-2000-017-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2000-017-5/}
}
TY  - JOUR
AU  - Granville, Andrew
AU  - Mollin, R. A.
AU  - Williams, H. C.
TI  - An Upper Bound on the Least Inert Prime in a Real Quadratic Field
JO  - Canadian journal of mathematics
PY  - 2000
SP  - 369
EP  - 380
VL  - 52
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2000-017-5/
DO  - 10.4153/CJM-2000-017-5
ID  - 10_4153_CJM_2000_017_5
ER  - 
%0 Journal Article
%A Granville, Andrew
%A Mollin, R. A.
%A Williams, H. C.
%T An Upper Bound on the Least Inert Prime in a Real Quadratic Field
%J Canadian journal of mathematics
%D 2000
%P 369-380
%V 52
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2000-017-5/
%R 10.4153/CJM-2000-017-5
%F 10_4153_CJM_2000_017_5

[1] [1] Bach, E., Explicit bounds for primality testing and related problems. Math. Comp. 55(1990), 355–380. Google Scholar

[2] [2] Burgess, D. A., n character sums and L-series, I. Proc. LondonMath. Soc. 12(1962), 193–206. Google Scholar

[3] [3] Davenport, H., Multiplicative Number Theory. 2nd edn, Springer-Verlag, New York, 1980. Google Scholar

[4] [4] Lukes, R. F., Patterson, C. D. and Williams, H. C., Some results on pseudosquares. Math. Comp. 65(1996), 361–372. Google Scholar

[5] [5] Mollin, R. A., Quadratics. CRC Press, Boca Raton, 1995. Google Scholar

[6] [6] Norton, K. K., Bounds for sequences of consecutive power residues. Analytic Number Theory, Proc. Sympos. Pure Math. 24, Amer.Math. Soc., Providence, RI, 1973, 213–220. Google Scholar

[7] [7] Rosser, J. B. and Schoenfeld, L., Approximate formulae for some functions of prime numbers. Illinois J. Math. 6(1962), 64–94. Google Scholar

[8] [8] Schoenfeld, L., Sharper bounds for the Chebyshev functions θ(x) and ψ(x). Math. Comp. 30(1976), 337–360. 900. Google Scholar

[9] [9] Western, A. E. and Miller, J. C. P., Tables of Indices and Primitive Roots. Royal Society, Cambridge, 1968. Google Scholar

Cité par Sources :