Summation of Series Defined by Counting Blocks of Digits

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dc.creatorAllouche, Jean-Paul
dc.creatorShallit, Jeffrey
dc.creatorSondow, Jonathan
dc.date2005-12-16
dc.date2006-06-02
dc.date.accessioned2026-07-07T07:42:18Z
dc.date.available2026-07-07T07:42:18Z
dc.descriptionWe discuss the summation of certain series defined by counting blocks of digits in the $B$-ary expansion of an integer. For example, if $s_2(n)$ denotes the sum of the base-2 digits of $n$, we show that $\sum_{n \geq 1} s_2(n)/(2n(2n+1)) = (γ+ \log \frac{4}π)/2$. We recover this previous result of Sondow in math.NT/0508042 and provide several generalizations.
dc.description12 pages, Introduction expanded, references added, accepted by J. Number Theory
dc.identifierhttps://arxiv.org/abs/math/0512399
dc.identifierhttp://arxiv.org/abs/math/0512399
dc.identifierJournal of Number Theory 123 (2007) 133-143
dc.identifierdoi:10.1016/j.jnt.2006.06.001
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/122397
dc.subjectNumber Theory
dc.subject11A63, 11Y60
dc.titleSummation of Series Defined by Counting Blocks of Digits
dc.typetext

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