A Lower Bound on the Number of Cyclic Function Fields With Class Number Divisible by n
Canadian mathematical bulletin, Tome 49 (2006) no. 3, pp. 448-463

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

In this paper, we find a lower bound on the number of cyclic function fields of prime degree $l$ whose class numbers are divisible by a given integer $n$ . This generalizes a previous result of D. Cardon and R. Murty which gives a lower bound on the number of quadratic function fields with class numbers divisible by $n$ .
DOI : 10.4153/CMB-2006-044-7
Mots-clés : 11R29, 11R58
Pacelli, Allison M. A Lower Bound on the Number of Cyclic Function Fields With Class Number Divisible by n. Canadian mathematical bulletin, Tome 49 (2006) no. 3, pp. 448-463. doi: 10.4153/CMB-2006-044-7
@article{10_4153_CMB_2006_044_7,
     author = {Pacelli, Allison M.},
     title = {A {Lower} {Bound} on the {Number} of {Cyclic} {Function} {Fields} {With} {Class} {Number} {Divisible} by n},
     journal = {Canadian mathematical bulletin},
     pages = {448--463},
     year = {2006},
     volume = {49},
     number = {3},
     doi = {10.4153/CMB-2006-044-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-044-7/}
}
TY  - JOUR
AU  - Pacelli, Allison M.
TI  - A Lower Bound on the Number of Cyclic Function Fields With Class Number Divisible by n
JO  - Canadian mathematical bulletin
PY  - 2006
SP  - 448
EP  - 463
VL  - 49
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-044-7/
DO  - 10.4153/CMB-2006-044-7
ID  - 10_4153_CMB_2006_044_7
ER  - 
%0 Journal Article
%A Pacelli, Allison M.
%T A Lower Bound on the Number of Cyclic Function Fields With Class Number Divisible by n
%J Canadian mathematical bulletin
%D 2006
%P 448-463
%V 49
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-044-7/
%R 10.4153/CMB-2006-044-7
%F 10_4153_CMB_2006_044_7

[1] [1] Byeon, D. and Koh, E., Real quadratic fields with class number divisible by 3. Manuscripta Math. 111(2003), no. 2, 261–263. Google Scholar

[2] [2] Cardon, D. and Ram Murty, R., Exponents of class groups of quadratic function fields over finite fields. Canad. Math. Bull. 44(2001), no. 4, 398–407. Google Scholar

[3] [3] Chakraborty, K. and Ram Murty, M., On the number of real quadratic fields with class number divisible by 3. Proc. Amer. Math. Soc. 131(2003), no. 1, 41–44. Google Scholar

[4] [4] Cohen, H. and Lenstra, H. W. Jr., Heuristics on class groups of number fields. In: Number Theory, Lecture Notes in Math. 1068, Springer, Berlin, 1984, pp. 33–62. Google Scholar

[5] [5] Cohen, H. and Martinet, J., Class groups of number fields: numerical heuristics. Math. Comp. 48(1987), no. 177, 123–137. Google Scholar

[6] [6] Friedman, E. and Washington, L. C., On the distribution of divisor class groups of curves over a finite field. In: Théorie des nombres, de Gruyter, Berlin, 1989, pp. 227–239. Google Scholar

[7] [7] Friesen, C., Class number divisibility in real quadratic function fields. Canad. Math. Bull. 35(1992), no. 3, 361–370. Google Scholar

[8] [8] Gauss, C. F., Disquisitiones Arithmeticae. Leipzig, 1801. Google Scholar

[9] [9] Kummer, E., Beweis des Fermat’schen Satzes der Unmöglichkeit von xλ + yλ = zλ für eine unendliche [sic] Anzahl Primzahlen λ . Monatsber. Akad. Wiss. Berlin, 1847, 132–141, 305-319. Google Scholar

[10] [10] Luca, F., A note on the divisibility of class numbers of real quadratic fields. C. R. Math. Acad. Sci. Soc. R. Can. 25(2003), no. 3, 71–75. Google Scholar

[11] [11] Murty, M. R., Exponents of class groups of quadratic fields. In: Topics in Number Theory, Math. Appl. 467, Kluwer Academic. Publishers, Dordrecht, 1999, pp. 229–239. Google Scholar

[12] [12] Nagell, T., Uber die Klassenzahl imaginar quadratischer Zahlkorper. Abh. Math. Sem. Univ. Hamburg 1(1922), 140–150. Google Scholar

[13] [13] Rosen, M., Average value of class numbers in cyclic extensions of the rational function field. In: Number Theory, CMS Conf. Proc. 15, American Mathematical Society, Providence, RI, 1995, pp. 307–323. Google Scholar

[14] [14] Soundararajan, K., Divisibility of class numbers of imaginary quadratic fields. J. London Math. Soc. 61(2000), no. 3, 681–690. Google Scholar

[15] [15] Yamamoto, Y., On unramified Galois extensions of quadratic number fields. Osaka J. Math. 7(1970), 57–76. Google Scholar

[16] [16] Yu, G., A note on the divisibility of class numbers of real quadratic fields. J. Number Theory 97(2002), no. 1, 35–44. Google Scholar

Cité par Sources :