A group-invariant version of Lehmer's conjecture on heights

Jan Willem M van Ittersum

doi:10.1016/j.jnt.2016.07.015

A group-invariant version of Lehmer's conjecture on heights

Jan Willem M van Ittersum

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

Abstract

We state and prove a group-invariant version of Lehmer's conjecture on heights, generalizing papers by Zagier (1993) [5] and Dresden (1998) [1] which are special cases of this theorem. We also extend their three cases to a full classification of all finite cyclic groups satisfying the condition that the set of all orbits for which every non-zero element lies on the unit circle is finite and non-empty.

Original language	English
Pages (from-to)	145-154
Number of pages	10
Journal	Journal of Number Theory
Volume	171
DOIs	https://doi.org/10.1016/j.jnt.2016.07.015
Publication status	Published - 1 Feb 2017

Keywords

G-orbit height
Lehmer's conjecture
Mahler measure
Weil height

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10.1016/j.jnt.2016.07.015

1-s2.0-S0022314X16301986-mainFinal published version, 280 KBLicence: Taverne

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title = "A group-invariant version of Lehmer's conjecture on heights",

abstract = "We state and prove a group-invariant version of Lehmer's conjecture on heights, generalizing papers by Zagier (1993) [5] and Dresden (1998) [1] which are special cases of this theorem. We also extend their three cases to a full classification of all finite cyclic groups satisfying the condition that the set of all orbits for which every non-zero element lies on the unit circle is finite and non-empty.",

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AB - We state and prove a group-invariant version of Lehmer's conjecture on heights, generalizing papers by Zagier (1993) [5] and Dresden (1998) [1] which are special cases of this theorem. We also extend their three cases to a full classification of all finite cyclic groups satisfying the condition that the set of all orbits for which every non-zero element lies on the unit circle is finite and non-empty.

KW - G-orbit height

KW - Lehmer's conjecture

KW - Mahler measure

KW - Weil height

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JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

A group-invariant version of Lehmer's conjecture on heights

Abstract

Keywords

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