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On multiplicatively dependent vectors of algebraic numbers


Authors: Francesco Pappalardi, Min Sha, Igor E. Shparlinski and Cameron L. Stewart
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 11N25, 11R04
DOI: https://doi.org/10.1090/tran/7115
Published electronically: February 1, 2018
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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.


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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
Email: shamin2010@gmail.com

Igor E. Shparlinski
Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
Email: igor.shparlinski@unsw.edu.au

Cameron L. Stewart
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada
Email: cstewart@uwaterloo.ca

DOI: https://doi.org/10.1090/tran/7115
Keywords: Multiplicatively dependent vectors, divisors, smooth numbers, naive height, Weil height
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.
Article copyright: © Copyright 2018 American Mathematical Society

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