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P. Schmitt C. Krattenthaler H. Rindler J. Schoissengeier H. Mitsch H. Muthsam R. Bürger 《Monatshefte für Mathematik》1996,121(4):399-404
Ohne Zusammenfassung 相似文献
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J. Schoissengeier 《Monatshefte für Mathematik》2000,129(2):147-151
Let x be a real number, α an irrational number with continued fraction expansion and convergents a positive integer, be chosen such that the fractional part of x and J. Beck [1] proved that We give a shorter proof, thereby using Dedekind sums. We may (and do) assume w.l.o.g. that .
There are non-negative integers such that
and (the so-called Ostrowski-expansion of N with respect to α). Let us put for and, for . Then . Let us finally put and, for and .
(Received 1 March 1999) 相似文献
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Johannes Schoissengeier 《Mathematische Annalen》1993,296(1):529-545
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We consider the g-ary expansion N=∑ k b k (N, g)g k of non-negative integers N and prove various results on the distribution and the mean value of the k-th digit b k (N, g) if g varies in an interval of the form 2≤g≤N η. As an application we also consider the average value of the sum-of-digits function s(N, g)=∑ k b k (N, g). 相似文献