Geodesic
A Generalization of the Turán Theorem and Its Applications
Canadian mathematical bulletin, Tome 47 (2004) no. 4, pp. 573-588

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

We axiomatize the main properties of the classical Turán Theorem in order to apply it to a general context. We provide applications in the cases of number fields, function fields, and geometrically irreducible varieties over a finite field.
DOI : 10.4153/CMB-2004-056-7
Mots-clés : 11N37, 11N80 
Liu, Yu-Ru. A Generalization of the Turán Theorem and Its Applications. Canadian mathematical bulletin, Tome 47 (2004) no. 4, pp. 573-588. doi: 10.4153/CMB-2004-056-7
@article{10_4153_CMB_2004_056_7,
     author = {Liu, Yu-Ru},
     title = {A {Generalization} of the {Tur\'an} {Theorem} and {Its} {Applications}},
     journal = {Canadian mathematical bulletin},
     pages = {573--588},
     year = {2004},
     volume = {47},
     number = {4},
     doi = {10.4153/CMB-2004-056-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-056-7/}
}
TY  - JOUR
AU  - Liu, Yu-Ru
TI  - A Generalization of the Turán Theorem and Its Applications
JO  - Canadian mathematical bulletin
PY  - 2004
SP  - 573
EP  - 588
VL  - 47
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-056-7/
DO  - 10.4153/CMB-2004-056-7
ID  - 10_4153_CMB_2004_056_7
ER  - 
%0 Journal Article
%A Liu, Yu-Ru
%T A Generalization of the Turán Theorem and Its Applications
%J Canadian mathematical bulletin
%D 2004
%P 573-588
%V 47
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-056-7/
%R 10.4153/CMB-2004-056-7
%F 10_4153_CMB_2004_056_7

[1] [1] Elliott, P. D. T. A., Probabilistic number theory, I, II. Springer-Verlag, New York, 1979. Google Scholar

[2] [2] Hartshorne, R., Algebraic geometry. Springer Verlag, New York, 1977. Google Scholar

[3] [3] Hardy, G. H. and Ramanujan, S., The normal number of prime factors of number n. Quar. J. Pure Appl. Math. 48 (1917), 76–97 Google Scholar

[4] [4] Liu, Y.-R. and Murty, M. R., The Turán sieve method and some of its applications. J. RamanujanMath. Soc. 14 (1999), 21–35. Google Scholar

[5] [5] Lorenzini, D., An invitation to arithmetic geometry. Graduate Studies in Mathematics, 9, American Mathematics Society, Providence, RI, 1996. Google Scholar

[6] [6] Lang, S. & Weil, A., Number of points of varieties in finite fields. Am. J. Math. 76 (1954), 819–827. Google Scholar

[7] [7] Mertens, F., Ein Beitrag zur analytischen Zahlentheorie. J. Reine Angew.Math. 78 (1874), 46–62. Google Scholar

[8] [8] Murty, M. R., Problems in analytic number theory. Springer-Verlag, New York, 2001. Google Scholar

[9] [9] Prachar, K., Verallgemeinerung eines satzes von Hardy and Ramanujan auf algebraische zahlkörper. Monatsh.Math. 56 (1952), 229–232. Google Scholar

[10] [10] Rosen, M., Number theory in Function Fields. Lecture notes given at K.A.I.S.T., Taejon, Korea, 1994. Google Scholar

[11] [11] Saidak, F., On a theorem of Hardy-Ramanujan-Turán I, to appear. Google Scholar

[12] [12] Turán, P., On a theorem of Hardy and Ramanujan. J. LondonMath. Soc. 9 (1934), 274–276. Google Scholar

[13] [13] Weber, H., Über zahlengruppen in algebraischen körpern. Math. Ann. 49 (1897), 83–100. Google Scholar

Cité par Sources :