On multiplicatively dependent vectors of algebraic numbers
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- by Francesco Pappalardi, Min Sha, Igor E. Shparlinski and Cameron L. Stewart PDF
- Trans. Amer. Math. Soc. 370 (2018), 6221-6244 Request permission
Abstract:
In this paper, we give several asymptotic formulas for the number of multiplicatively dependent vectors of algebraic numbers of fixed degree, or within a fixed number field, and bounded height.References
Additional Information
- Francesco Pappalardi
- Affiliation: Dipartimento di Matematica e Fisica, Università Roma Tre, Roma, I–00146, Italy
- Email: pappa@mat.uniroma3.it
- Min Sha
- Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
- MR Author ID: 937863
- Email: shamin2010@gmail.com
- Igor E. Shparlinski
- Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
- MR Author ID: 192194
- Email: igor.shparlinski@unsw.edu.au
- Cameron L. Stewart
- Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada
- MR Author ID: 167235
- Email: cstewart@uwaterloo.ca
- Received by editor(s): June 28, 2016
- Received by editor(s) in revised form: November 2, 2016
- Published electronically: February 1, 2018
- Additional Notes: The first author was supported in part by Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni from Istituto Nazionale di Alta Matematica “F. Severi”.
The research of the second and third authors was supported by the Australian Research Council Grant DP130100237.
The research of the fourth author was supported in part by the Canada Research Chairs Program and by Grant A3528 from the Natural Sciences and Engineering Research Council of Canada. - © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 6221-6244
- MSC (2010): Primary 11N25, 11R04
- DOI: https://doi.org/10.1090/tran/7115
- MathSciNet review: 3814329