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Martin Widmer
Small generators of function fields
Journal de théorie des nombres de Bordeaux, 22 no. 3 (2010), p. 747-753, doi: 10.5802/jtnb.744
Article PDF | Reviews MR 2769343
[1] E. Artin, Algebraic numbers and algebraic functions, Gordon and Breach, New York, 1967 MR 237460 | Zbl 0194.35301
[2] E. Bombieri & W. Gubler, Heights in Diophantine Geometry, Cambridge University Press, 2006 MR 2216774 | Zbl 1115.11034
[3] W. Duke, Hyperbolic distribution problems and half-integral weight Masss forms, Invent. Math. 92 (1988), p. 73-90 MR 931205 | Zbl 0628.10029
[4] J. Ellenberg & A. Venkatesh, Reflection principles and bounds for class group torsion, Int. Math. Res. Not. no.1, Art. ID rnm002 (2007) MR 2331900 | Zbl 1130.11060
[5] K. Mahler, An inequality for the discriminant of a polynomial, Michigan Math. J. 11 (1964), p. 257-262
Article | MR 166188 | Zbl 0135.01702
[6] D. Roy & J. L. Thunder, A note on Siegel’s lemma over number fields, Monatsh. Math. 120 (1995), p. 307-318 MR 1363143 | Zbl 0839.11011
[7] W. Ruppert, Small generators of number fields, Manuscripta math. 96 (1998), p. 17-22 MR 1624340 | Zbl 0899.11063
[8] J. Silverman, Lower bounds for height functions, Duke Math. J. 51 (1984), p. 395-403
Article | MR 747871 | Zbl 0579.14035
[9] H. Stichtenoth, Algebraic function fields and codes, Springer, 1993 MR 1251961 | Zbl 0816.14011
[10] J. L. Thunder, Siegel’s lemma for function fields, Michigan Math. J. 42 (1995), p. 147-162
Article | MR 1322196 | Zbl 0830.11024
[11] J. D. Vaaler & M. Widmer, On small generators of number fields, in preparation (2010)
Martin Widmer
Small generators of function fields
Journal de théorie des nombres de Bordeaux, 22 no. 3 (2010), p. 747-753, doi: 10.5802/jtnb.744
Article PDF | Reviews MR 2769343
Résumé - 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.
Bibliography
[2] E. Bombieri & W. Gubler, Heights in Diophantine Geometry, Cambridge University Press, 2006 MR 2216774 | Zbl 1115.11034
[3] W. Duke, Hyperbolic distribution problems and half-integral weight Masss forms, Invent. Math. 92 (1988), p. 73-90 MR 931205 | Zbl 0628.10029
[4] J. Ellenberg & A. Venkatesh, Reflection principles and bounds for class group torsion, Int. Math. Res. Not. no.1, Art. ID rnm002 (2007) MR 2331900 | Zbl 1130.11060
[5] K. Mahler, An inequality for the discriminant of a polynomial, Michigan Math. J. 11 (1964), p. 257-262
Article | MR 166188 | Zbl 0135.01702
[6] D. Roy & J. L. Thunder, A note on Siegel’s lemma over number fields, Monatsh. Math. 120 (1995), p. 307-318 MR 1363143 | Zbl 0839.11011
[7] W. Ruppert, Small generators of number fields, Manuscripta math. 96 (1998), p. 17-22 MR 1624340 | Zbl 0899.11063
[8] J. Silverman, Lower bounds for height functions, Duke Math. J. 51 (1984), p. 395-403
Article | MR 747871 | Zbl 0579.14035
[9] H. Stichtenoth, Algebraic function fields and codes, Springer, 1993 MR 1251961 | Zbl 0816.14011
[10] J. L. Thunder, Siegel’s lemma for function fields, Michigan Math. J. 42 (1995), p. 147-162
Article | MR 1322196 | Zbl 0830.11024
[11] J. D. Vaaler & M. Widmer, On small generators of number fields, in preparation (2010)
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ISSN : 2118-8572 (online) 1246-7405 (print)
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Société Arithmétique de Bordeaux