Small generators of function fields

Martin Widmer[1]

  • [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

Abstract

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Let 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.

How to cite

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Widmer, 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

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  1. E. Artin, Algebraic numbers and algebraic functions, (1967), Gordon and Breach, New York Zbl0194.35301MR237460
  2. E. Bombieri, W. Gubler, Heights in Diophantine Geometry, (2006), Cambridge University Press Zbl1115.11034MR2216774
  3. W. Duke, Hyperbolic distribution problems and half-integral weight Masss forms, Invent. Math. 92 (1988), 73-90 Zbl0628.10029MR931205
  4. J. Ellenberg, A. Venkatesh, Reflection principles and bounds for class group torsion, Int. Math. Res. Not. no.1, Art. ID rnm002 (2007) Zbl1130.11060MR2331900
  5. K. Mahler, An inequality for the discriminant of a polynomial, Michigan Math. J. 11 (1964), 257-262 Zbl0135.01702MR166188
  6. D. Roy, J. L. Thunder, A note on Siegel’s lemma over number fields, Monatsh. Math. 120 (1995), 307-318 Zbl0839.11011MR1363143
  7. W. Ruppert, Small generators of number fields, Manuscripta math. 96 (1998), 17-22 Zbl0899.11063MR1624340
  8. J. Silverman, Lower bounds for height functions, Duke Math. J. 51 (1984), 395-403 Zbl0579.14035MR747871
  9. H. Stichtenoth, Algebraic function fields and codes, (1993), Springer Zbl0816.14011MR1251961
  10. J. L. Thunder, Siegel’s lemma for function fields, Michigan Math. J. 42 (1995), 147-162 Zbl0830.11024MR1322196
  11. J. D. Vaaler, M. Widmer, On small generators of number fields, in preparation (2010) Zbl1307.11108

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