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On the number of rational iterated preimages of the origin under quadratic dynamical systems

Titelangaben

Faber, Xander ; Hutz, Benjamin ; Stoll, Michael:
On the number of rational iterated preimages of the origin under quadratic dynamical systems.
In: International Journal of Number Theory. Bd. 7 (2011) Heft 7 . - S. 1781-1806.
ISSN 1793-0421
DOI: 10.1142/S1793042111004162

Volltext

Link zum Volltext (externe URL): Volltext

Angaben zu Projekten

Projektfinanzierung: The first author was supported by a National Science Foundation Postdoctoral Research Fellowship during part of this work.

Abstract

For a quadratic endomorphism of the affine line defined over the rationals, we consider the problem of bounding the number of rational points that eventually land at the origin after iteration. In the article "Uniform bounds on pre-images under quadratic dynamical systems," by two of the present authors and five others, it was shown that the number of rational iterated preimages of the origin is bounded as one varies the morphism in a certain one-dimensional family. Subject to the validity of the Birch and Swinnerton-Dyer conjecture and some other related conjectures for the L-series of a specific abelian variety and using a number of modern tools for locating rational points on high genus curves, we show that the maximum number of rational iterated preimages is six. We also provide further insight into the geometry of the "preimage curves."

Weitere Angaben

Publikationsform: Artikel in einer Zeitschrift
Begutachteter Beitrag: Ja
Institutionen der Universität: Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik II (Computeralgebra)
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik II (Computeralgebra) > Lehrstuhl Mathematik II (Computeralgebra) - Univ.-Prof. Dr. Michael Stoll
Fakultäten
Fakultäten > Fakultät für Mathematik, Physik und Informatik
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut
Titel an der UBT entstanden: Ja
Themengebiete aus DDC: 500 Naturwissenschaften und Mathematik > 510 Mathematik
Eingestellt am: 28 Nov 2014 11:11
Letzte Änderung: 10 Dec 2014 12:27
URI: https://eref.uni-bayreuth.de/id/eprint/4262