Small generators of function fields
- [1] Institut für Mathematik A Technische Universität Graz Steyrergasse 30/II 8010 Graz, Austria
Journal de Théorie des Nombres de Bordeaux (2010)
- Volume: 22, Issue: 3, page 747-753
- ISSN: 1246-7405
Access Full Article
topAbstract
topHow to cite
topWidmer, Martin. "Small generators of function fields." Journal de Théorie des Nombres de Bordeaux 22.3 (2010): 747-753. <http://eudml.org/doc/116432>.
@article{Widmer2010,
abstract = {Let $\mathbb\{K\}/k$ be a finite extension of a global field. Such an extension can be generated over $k$ by a single element. The aim of this article is to prove the existence of a ”small” generator in the function field case. This answers the function field version of a question of Ruppert on small generators of number fields.},
affiliation = {Institut für Mathematik A Technische Universität Graz Steyrergasse 30/II 8010 Graz, Austria},
author = {Widmer, Martin},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {function field; small generator; Weil bounds},
language = {eng},
number = {3},
pages = {747-753},
publisher = {Université Bordeaux 1},
title = {Small generators of function fields},
url = {http://eudml.org/doc/116432},
volume = {22},
year = {2010},
}
TY - JOUR
AU - Widmer, Martin
TI - Small generators of function fields
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2010
PB - Université Bordeaux 1
VL - 22
IS - 3
SP - 747
EP - 753
AB - Let $\mathbb{K}/k$ be a finite extension of a global field. Such an extension can be generated over $k$ by a single element. The aim of this article is to prove the existence of a ”small” generator in the function field case. This answers the function field version of a question of Ruppert on small generators of number fields.
LA - eng
KW - function field; small generator; Weil bounds
UR - http://eudml.org/doc/116432
ER -
References
top- E. Artin, Algebraic numbers and algebraic functions, (1967), Gordon and Breach, New York Zbl0194.35301MR237460
- E. Bombieri, W. Gubler, Heights in Diophantine Geometry, (2006), Cambridge University Press Zbl1115.11034MR2216774
- W. Duke, Hyperbolic distribution problems and half-integral weight Masss forms, Invent. Math. 92 (1988), 73-90 Zbl0628.10029MR931205
- J. Ellenberg, A. Venkatesh, Reflection principles and bounds for class group torsion, Int. Math. Res. Not. no.1, Art. ID rnm002 (2007) Zbl1130.11060MR2331900
- K. Mahler, An inequality for the discriminant of a polynomial, Michigan Math. J. 11 (1964), 257-262 Zbl0135.01702MR166188
- D. Roy, J. L. Thunder, A note on Siegel’s lemma over number fields, Monatsh. Math. 120 (1995), 307-318 Zbl0839.11011MR1363143
- W. Ruppert, Small generators of number fields, Manuscripta math. 96 (1998), 17-22 Zbl0899.11063MR1624340
- J. Silverman, Lower bounds for height functions, Duke Math. J. 51 (1984), 395-403 Zbl0579.14035MR747871
- H. Stichtenoth, Algebraic function fields and codes, (1993), Springer Zbl0816.14011MR1251961
- J. L. Thunder, Siegel’s lemma for function fields, Michigan Math. J. 42 (1995), 147-162 Zbl0830.11024MR1322196
- J. D. Vaaler, M. Widmer, On small generators of number fields, in preparation (2010) Zbl1307.11108
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.