Quadratic Non-Residues and Prime-Producing Polynomials
Canadian mathematical bulletin, Tome 32 (1989) no. 4, pp. 474-478

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

We will be looking at quadratic polynomials having positive discriminant and having a long string of primes as initial values. We find conditions tantamount to this phenomenon involving another long string of primes for which the discriminant of the polynomial is a quadratic non-residue. Using the generalized Riemann hypothesis (GRH) we are able to determine all discriminants satisfying this connection.
DOI : 10.4153/CMB-1989-068-1
Mots-clés : 12A20, 12A25
Mollin, R. A.; Williams, H. C. Quadratic Non-Residues and Prime-Producing Polynomials. Canadian mathematical bulletin, Tome 32 (1989) no. 4, pp. 474-478. doi: 10.4153/CMB-1989-068-1
@article{10_4153_CMB_1989_068_1,
     author = {Mollin, R. A. and Williams, H. C.},
     title = {Quadratic {Non-Residues} and {Prime-Producing} {Polynomials}},
     journal = {Canadian mathematical bulletin},
     pages = {474--478},
     year = {1989},
     volume = {32},
     number = {4},
     doi = {10.4153/CMB-1989-068-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1989-068-1/}
}
TY  - JOUR
AU  - Mollin, R. A.
AU  - Williams, H. C.
TI  - Quadratic Non-Residues and Prime-Producing Polynomials
JO  - Canadian mathematical bulletin
PY  - 1989
SP  - 474
EP  - 478
VL  - 32
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1989-068-1/
DO  - 10.4153/CMB-1989-068-1
ID  - 10_4153_CMB_1989_068_1
ER  - 
%0 Journal Article
%A Mollin, R. A.
%A Williams, H. C.
%T Quadratic Non-Residues and Prime-Producing Polynomials
%J Canadian mathematical bulletin
%D 1989
%P 474-478
%V 32
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1989-068-1/
%R 10.4153/CMB-1989-068-1
%F 10_4153_CMB_1989_068_1

[1] 1. Euler, E., Mem de Berlin, année 1722, 36; Comm. Arith. 1, 384. Google Scholar

[2] 2. Goldfeld, D., Gauss’ Glass Number Problem for Imaginary Quadratic Fields, Bull. Amer. Math. Soc. (New Series) 13 (1985), 23–37. Google Scholar

[3] 3. Mollin, R., Necessary and Sufficient Conditions for the Class Number of a Real Quadratic Field to be One, and a Conjecture of S. Chowla, Proceedings Amer. Math. Soc. 102 (1988), 17–21. Google Scholar

[4] 4. Mollin, R., Class Number One Criteria for Real Quadratic Fields I, Proceedings Japan Acad. Ser. A. 63 (1987), 121–125. Google Scholar

[5] 5. Mollin, R. and H. Williams, A Conjecture of S. Chowla via the Generalized Riemann Hypothesis, Proceedings Amer. Math. Soc. 102 (1988), 794–796. Google Scholar

[6] 6. Mollin, R. and H. Williams, On Prime-Valued Polynomials and Class Numbers of Real Quadratic Fields, Nagoya Math. J. 112 (1988), 143–151. Google Scholar

[7] 7. Mollin, R. and H. Williams, Prime Producing Quadratic Polynomials and Real Quadratic Fields of Class Number One (to appear: Proceedings of the International Number Theory Conference at Quebec City, July 1987). Google Scholar

[8] 8. Oesterlé, Versions effectives du theorem de Chebotarev sous LHypothèse de Riemann Généralisé, Soc. Math. France Astérisque 61 (1979), 165–167. Google Scholar

[9] 9. Patterson, C. D. and H. C. Williams, A report on the University of Manitoba Sieve Unit, Congresses Numerantium 37 (1983), 85–98. Google Scholar

[10] 10. Rosser, J. B. and L. Schoenfeld, Approximate Formulas for Some Functions of Prime Numbers, Illinois J. Math. 6 (1962), 64–94. Google Scholar

Cité par Sources :