On multiplicatively dependent vectors of algebraic numbers

Francesco Pappalardi; Min Sha; Igor E. Shparlinski; Cameron L. Stewart

doi:10.1090/tran/7115

On multiplicatively dependent vectors of algebraic numbers

Francesco Pappalardi, Min Sha, Igor E. Shparlinski, Cameron L. Stewart

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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.

Original language	English
Pages (from-to)	6221-6244
Number of pages	24
Journal	Transactions of the American Mathematical Society
Volume	370
Issue number	9
Early online date	2016
DOIs	https://doi.org/10.1090/tran/7115
Publication status	Published - Sep 2018
Externally published	Yes

Keywords

multiplicatively dependent vectors
divisors
smooth numbers
naive height
weil height

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10.1090/tran/7115

Cite this

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title = "On multiplicatively dependent vectors of algebraic numbers",

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.",

keywords = "multiplicatively dependent vectors, divisors, smooth numbers, naive height, weil height",

author = "Francesco Pappalardi and Min Sha and Shparlinski, {Igor E.} and Stewart, {Cameron L.}",

year = "2018",

month = sep,

doi = "10.1090/tran/7115",

language = "English",

volume = "370",

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AU - Pappalardi, Francesco

AU - Sha, Min

AU - Shparlinski, Igor E.

AU - Stewart, Cameron L.

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Y1 - 2018/9

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KW - multiplicatively dependent vectors

KW - divisors

KW - smooth numbers

KW - naive height

KW - weil height

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U2 - 10.1090/tran/7115

DO - 10.1090/tran/7115

M3 - Article

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EP - 6244

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 9

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On multiplicatively dependent vectors of algebraic numbers

Abstract

Keywords

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