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We consider the -ary digital expansion of the first terms of an exponential sequence . Using a result due to Kiss and Tichy [8], we prove that the average number of occurrences of an arbitrary digital block in the last digits is asymptotically equal to the expected value. Under stronger assumptions we get a similar result for the first digits, where is a positive constant. In both methods, we use estimations of exponential sums and the concept of discrepancy of real sequences modulo ...
On étudie la discrépance absolue de la suite de Farey d’ordre et on montre, en utilisant notamment une majoration d’une intégrale portant sur la fonction sommatoire de la fonction de Möbius, qu’elle est égale à exactement, ce qui est la valeur locale au point d’abscisse .
We consider sequences modulo one that are generated using a generalized polynomial over the real numbers. Such polynomials may also involve the integer part operation [·] additionally to addition and multiplication. A well studied example is the (nα) sequence defined by the monomial αx. Their most basic sister, , is less investigated. So far only the uniform distribution modulo one of these sequences is resolved. Completely new, however, are the discrepancy results proved in this paper. We show...
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