Counting algebraic units with bounded height

G. R. Everest; J. H. Loxton

doi:10.1006/jnth.1993.1047

Counting algebraic units with bounded height

G. R. Everest^*, J. H. Loxton

^*Corresponding author for this work

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

7 Citations (Scopus)

Abstract

Let K be an algebraic number field of degree d and let U denote its group of units. Suppose U has rank r and regulator R. Let U(q) denote the number of units in U with height less than q. We obtain an asymptotic formula for U(q) of the shape U(q) = A(log q)^r + O((log q)^{r - 1 - δ}), where δ is given explicitly in terms of d and R.

Original language	English
Pages (from-to)	222-227
Number of pages	6
Journal	Journal of Number Theory
Volume	44
Issue number	2
DOIs	https://doi.org/10.1006/jnth.1993.1047
Publication status	Published - Jun 1993

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title = "Counting algebraic units with bounded height",

abstract = "Let K be an algebraic number field of degree d and let U denote its group of units. Suppose U has rank r and regulator R. Let U(q) denote the number of units in U with height less than q. We obtain an asymptotic formula for U(q) of the shape U(q) = A(log q)r + O((log q)r - 1 - δ), where δ is given explicitly in terms of d and R.",

author = "Everest, {G. R.} and Loxton, {J. H.}",

year = "1993",

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doi = "10.1006/jnth.1993.1047",

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T1 - Counting algebraic units with bounded height

AU - Everest, G. R.

AU - Loxton, J. H.

PY - 1993/6

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N2 - Let K be an algebraic number field of degree d and let U denote its group of units. Suppose U has rank r and regulator R. Let U(q) denote the number of units in U with height less than q. We obtain an asymptotic formula for U(q) of the shape U(q) = A(log q)r + O((log q)r - 1 - δ), where δ is given explicitly in terms of d and R.

AB - Let K be an algebraic number field of degree d and let U denote its group of units. Suppose U has rank r and regulator R. Let U(q) denote the number of units in U with height less than q. We obtain an asymptotic formula for U(q) of the shape U(q) = A(log q)r + O((log q)r - 1 - δ), where δ is given explicitly in terms of d and R.

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U2 - 10.1006/jnth.1993.1047

DO - 10.1006/jnth.1993.1047

M3 - Article

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SN - 0022-314X

VL - 44

SP - 222

EP - 227

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 2

ER -

Counting algebraic units with bounded height

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