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Digital expansion of exponential sequences

Michael Fuchs (2002)

Journal de théorie des nombres de Bordeaux

We consider the q -ary digital expansion of the first N terms of an exponential sequence a n . 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 c log N digits is asymptotically equal to the expected value. Under stronger assumptions we get a similar result for the first ( log N ) 3 2 - ϵ digits, where ϵ is a positive constant. In both methods, we use estimations of exponential sums and the concept of discrepancy of real sequences modulo 1 ...

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