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Asymptotic analysis of a class of functional equations and applications

P. J. Grabner;  H. Prodinger;  R. F. Tichy — 1993

Journal de théorie des nombres de Bordeaux

Flajolet and Richmond have invented a method to solve a large class of divide-and-conquer recursions. The essential part of it is the asymptotic analysis of a certain generating function for z → ∞ by means of the Mellin transform. In this paper this type of analysis is performed for a reasonably large class of generating functions fulfilling a functional equation with polynomial coefficients. As an application, the average life time of a party of N people is computed, where each person advances one...

On the discrepancy of sequences associated with the sum-of-digits function

Gerhard Larcher;  N. Kopecek;  R. F. Tichy;  G. Turnwald — 1987

Annales de l'institut Fourier

If w = ( q k ) k ∈ N denotes the sequence of best approximation denominators to a real α , and s α ( n ) denotes the sum of digits of n in the digit representation of n to base w , then for all x irrational, the sequence ( s α ( n ) · x ) n ∈ N is uniformly distributed modulo one. Discrepancy estimates for the discrepancy of this sequence are given, which turn out to be best possible if α has bounded continued fraction coefficients.

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