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Gaps between logs
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2013 (English)In: Bulletin of the London Mathematical Society, ISSN 0024-6093, E-ISSN 1469-2120, Vol. 45, no 6, 1267-1280 p.Article in journal (Refereed) Published
Abstract [en]

We calculate the limiting gap distribution for the fractional parts of log n, where n runs through all positive integers. By rescaling the sequence, the proof quickly reduces to an argument used by Barra and Gaspard in the context of level spacing statistics for quantum graphs. The key ingredient is Weyl equidistribution of irrational translations on multi-dimensional tori. Our results extend to logarithms with arbitrary base; we deduce explicit formulas when the base is transcendental or the rth root of an integer. If the base is close to one, then the gap distribution is close to the exponential distribution.

Place, publisher, year, edition, pages
2013. Vol. 45, no 6, 1267-1280 p.
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URN: urn:nbn:se:uu:diva-213459DOI: 10.1112/blms/bdt060ISI: 000327508800014OAI: oai:DiVA.org:uu-213459DiVA: diva2:683539
Available from: 2014-01-04 Created: 2013-12-23 Last updated: 2014-01-04Bibliographically approved

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Strömbergsson, Andreas
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