Counting algebraic units with bounded height

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

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    6 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 languageEnglish
    Pages (from-to)222-227
    Number of pages6
    JournalJournal of Number Theory
    Volume44
    Issue number2
    DOIs
    Publication statusPublished - Jun 1993

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