The mixed Littlewood conjecture for pseudo-absolute values

Stephen Harrap, Alan Haynes*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

2 Citations (Scopus)

Abstract

In this paper we study the mixed Littlewood Conjecture with pseudo-absolute values. We show that if p is a prime and D is a pseudo-absolute value sequence satisfying mild conditions then

inf(n is an element of N) n vertical bar n vertical bar(p)vertical bar n vertical bar D parallel to n alpha parallel to = 0 for all alpha is an element of R.

Our proof relies on a measure rigidity theorem due to Lindenstrauss and lower bounds for linear forms in logarithms due to Baker and Wustholz. We also deduce the answer to the related metric question of how fast the infimum above tends to zero, for almost every alpha.

Original languageEnglish
Pages (from-to)941-960
Number of pages20
JournalMathematische Annalen
Volume357
Issue number3
DOIs
Publication statusPublished - Nov 2013

Keywords

  • INVARIANT-MEASURES
  • SET

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    Career Acceleration Fellowship

    Haynes, A. K.

    1/10/111/10/13

    Project: Research

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