Geodesic
On Minimal Sets of Generators for Primitive Roots
Canadian mathematical bulletin, Tome 38 (1995) no. 4, pp. 465-468

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

A conjecture of Brown and Zassenhaus (see [2]) states that the first log/? primes generate a primitive root (mod p) for almost all primes p. As a consequence of a Theorem of Burgess and Elliott (see [3]) it is easy to see that the first log2p log log4+∊p primes generate a primitive root (mod p) for almost all primes p. We improve this showing that the first log2 p/ log log p primes generate a primitive root (mod p) for almost all primes p.
DOI : 10.4153/CMB-1995-068-4
Mots-clés : 11N56, 11A07, sieve theory, primitive roots, Riemann hypothesis 
Pappalardi, Francesco. On Minimal Sets of Generators for Primitive Roots. Canadian mathematical bulletin, Tome 38 (1995) no. 4, pp. 465-468. doi: 10.4153/CMB-1995-068-4
@article{10_4153_CMB_1995_068_4,
     author = {Pappalardi, Francesco},
     title = {On {Minimal} {Sets} of {Generators} for {Primitive} {Roots}},
     journal = {Canadian mathematical bulletin},
     pages = {465--468},
     year = {1995},
     volume = {38},
     number = {4},
     doi = {10.4153/CMB-1995-068-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1995-068-4/}
}
TY  - JOUR
AU  - Pappalardi, Francesco
TI  - On Minimal Sets of Generators for Primitive Roots
JO  - Canadian mathematical bulletin
PY  - 1995
SP  - 465
EP  - 468
VL  - 38
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1995-068-4/
DO  - 10.4153/CMB-1995-068-4
ID  - 10_4153_CMB_1995_068_4
ER  - 
%0 Journal Article
%A Pappalardi, Francesco
%T On Minimal Sets of Generators for Primitive Roots
%J Canadian mathematical bulletin
%D 1995
%P 465-468
%V 38
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1995-068-4/
%R 10.4153/CMB-1995-068-4
%F 10_4153_CMB_1995_068_4

[1] 1. Bombieri, E., Le grande crible dans la théorie analytique des nombres, Astérisque 18(1974). Google Scholar

[2] 2. Brown, H. and Zassenhaus, H., Some empirical observation on primitive roots, J. Number Theory 3(1971) 306–309. Google Scholar

[3] 3. Burgess, D. A. and Elliott, P. D. T. A., The average of the least primitive root, Mathematika 15(1968), 39–50. Google Scholar

[4] 4. Canfield, E. R., Erdös, P. and Pomerance, C., On a problem of Oppenheim concerning “Factorization Numerorum ”, J. Number Theory 17(1983), 1–28. Google Scholar

[5] 5. Konyagin, S. and Pomerance, C., On primes recognizable in deterministic polynomial time, preprint. Google Scholar

Cité par Sources :