Ray class fields of global function fields with many rational places
Acta Arithmetica (2000)
- Volume: 95, Issue: 2, page 97-122
- ISSN: 0065-1036
Access Full Article
topHow to cite
topRoland Auer. "Ray class fields of global function fields with many rational places." Acta Arithmetica 95.2 (2000): 97-122. <http://eudml.org/doc/207447>.
@article{RolandAuer2000,
author = {Roland Auer},
journal = {Acta Arithmetica},
keywords = {ray class fields; global function fields; characteristic p; curves with many rational points; S-class numbers},
language = {eng},
number = {2},
pages = {97-122},
title = {Ray class fields of global function fields with many rational places},
url = {http://eudml.org/doc/207447},
volume = {95},
year = {2000},
}
TY - JOUR
AU - Roland Auer
TI - Ray class fields of global function fields with many rational places
JO - Acta Arithmetica
PY - 2000
VL - 95
IS - 2
SP - 97
EP - 122
LA - eng
KW - ray class fields; global function fields; characteristic p; curves with many rational points; S-class numbers
UR - http://eudml.org/doc/207447
ER -
References
top- [1] R. Auer, Ray class fields of global function fields with many rational places, Dissertation at the University of Oldenburg, www.bis.uni-oldenburg.de/dissertation/ediss.html, 1999. Zbl0930.11082
- [2] J. W. S. Cassels and A. Fröhlich, Algebraic Number Theory, Academic Press, New York, 1967. Zbl0153.07403
- [3] H. Cohen, F. Diaz y Diaz and M. Olivier, Computing ray class groups, conductors and discriminants, in: Algorithmic Number Theory, H. Cohen (ed.), Lecture Notes in Comput. Sci. 1122, Springer, 1996, 49-57. Zbl0898.11046
- [4] K M. Daberkow, C. Fieker, J. Klüners, M. Pohst, K. Roegner, M. Schörnig and K. Wildanger, KANT V4, J. Symbolic Comput. 24 (1997), 267-283.
- [5] R. Fuhrmann and F. Torres, The genus of curves over finite fields with many rational points, Manuscripta Math. 89 (1996), 103-106. Zbl0857.11032
- [6] A. Garcia and H. Stichtenoth, Algebraic function fields over finite fields with many rational places, IEEE Trans. Inform. Theory 41 (1995), 1548-1563. Zbl0863.11040
- [7] G. van der Geer and M. van der Vlugt, How to construct curves over finite fields with many points, in: Arithmetic Geometry (Cortona, 1984), F. Catanese (ed.), Cambridge Univ. Press, 1997, 169-189. Zbl0884.11027
- [8] G. van der Geer and M. van der Vlugt, Constructing curves over finite fields with many points by solving linear equations, preprint, 1997. Zbl1054.11506
- [9] G. van der Geer and M. van der Vlugt, Tables of curves with many points, preprint at http://www.wins.uva.nl/geer, 1999. Zbl0965.11028
- [10] H H. Hasse, Number Theory, Springer, Berlin, 1980.
- [11] D. R. Hayes, Explicit class field theory in global function fields, in: Studies in Algebra and Number Theory, Adv. in Math. Suppl. Stud. 6, Academic Press, 1979, 173-217.
- [12] H. Kisilevsky, Multiplicative independence in function fields, J. Number Theory 44 (1993), 352-355. Zbl0780.11058
- [13] K. Lauter, Ray class field constructions of curves over finite fields with many rational points, in: Algorithmic Number Theory, H. Cohen (ed.), Lecture Notes in Comput. Sci. 1122, Springer, 1996, 187-195. Zbl0935.11022
- [14] K. Lauter, Deligne-Lusztig curves as ray class fields, Manuscripta Math. 98 (1999), 87-96. Zbl0919.11076
- [15] K. Lauter, A formula for constructing curves over finite fields with many rational points, J. Number Theory 74 (1999), 56-72. Zbl1044.11054
- [16] J. Neukirch, Algebraische Zahlentheorie, Springer, Berlin, 1991.
- [17] H. Niederreiter, Nets, (t,s)-sequences, and algebraic curves over finite fields with many rational points, in: Proc. Internat. Congress of Math. (Berlin, 1998), Documenta Math. Extra Vol. ICM III (1998), 377-386. Zbl0899.11038
- [18] H. Niederreiter and C. P. Xing, Explicit global function fields over the binary field with many rational places, Acta Arith. 75 (1996), 383-396. Zbl0877.11065
- [19] H. Niederreiter and C. P. Xing, Cyclotomic function fields, Hilbert class fields, and global function fields with many rational places, ibid. 79 (1997), 59-76. Zbl0891.11057
- [20] H. Niederreiter and C. P. Xing, Drinfeld modules of rank 1 and algebraic curves with many rational points. II, ibid. 81 (1997), 81-100. Zbl0886.11033
- [21] H. Niederreiter and C. P. Xing, Algebraic curves over finite fields with many rational points, in: Proc. Number Theory Conf. (Eger, 1996), de Gruyter, 1998, 423-443. Zbl0923.11093
- [22] H. Niederreiter and C. P. Xing, Global function fields with many rational places over the ternary field, Acta Arith. 83 (1998), 65-86. Zbl1102.11312
- [23] H. Niederreiter and C. P. Xing, Global function fields with many rational places over the quinary field, Demonstratio Math. 30 (1997), 919-930. Zbl0958.11075
- [24] H. Niederreiter and C. P. Xing, Global function fields with many rational places over the quinary field. II, Acta Arith. 86 (1998), 277-288. Zbl0922.11098
- [25] H. Niederreiter and C. P. Xing, Algebraic curves with many rational points over finite fields of characteristic 2, in: Number Theory in Progress (Zakopane, 1997), Vol. 1, de Gruyter, 1999, 359-380. Zbl0935.11021
- [26] H. Niederreiter and C. P. Xing, A general method of constructing global function fields with many rational places, in: Algorithmic Number Theory (Portland, 1998), Lecture Notes in Comput. Sci. 1423, Springer, 1998, 555-566. Zbl0909.11052
- [27] H. Niederreiter and C. P. Xing, Algebraic curves over finite fields with many rational points and their applications, in: Number Theory, V. C. Dumir et al. (eds.), Indian National Science Academy, to appear. Zbl0986.11040
- [28] H. Niederreiter and C. P. Xing, Global function fields with many rational places and their applications, Contemp. Math. 225 (1999), 87-111. Zbl0960.11033
- [29] J. P. Pedersen, A function field related to the Ree group, in: Coding Theory and Algebraic Geometry (Luminy, 1991), H. Stichtenoth and M. A. Tsfasman (eds.), Lecture Notes in Math. 1518, Springer, Berlin, 1992, 122-131.
- [30] M. Perret, Tours ramifiées infinies de corps de classes, J. Number Theory 38 (1991), 300-322. Zbl0741.11044
- [31] M. Rosen, S-units and S-class group in algebraic function fields, J. Algebra 26 (1973), 98-108. Zbl0265.12003
- [32] M. Rosen, The Hilbert class field in function fields, Exposition. Math. 5 (1987), 365-378. Zbl0632.12017
- [33] R. Schoof, Algebraic Curves and Coding Theory, UTM 336 (1990), Univ. of Trento.
- [34] J.-P. Serre, Sur le nombre des points rationnelles d'une courbe algébrique sur un corps fini, C. R. Acad. Sci. Paris Sér. I 296 (1983), 397-402. Zbl0538.14015
- [35] J.-P. Serre, Nombres de points des courbes algébrique sur , Sém. Théor. Nombres Bordeaux 22 (1982/83).
- [36] J.-P. Serre, Résumé des cours de 1983-1984, Annuaire du Collège de France, 1984, 79-83.
- [37] H. Stichtenoth, Algebraic Function Fields and Codes, Springer, Berlin, 1993.
- [38] C. P. Xing and H. Niederreiter, Drinfel'd modules of rank 1 and algebraic curves with many rational points, Monatsh. Math. 127 (1999), 219-241. Zbl0982.11034
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.