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The sum-of-digits function of canonical number systems: Distribution in residue classes

✍ Scribed by Manfred G. Madritsch

Book ID
116673114
Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
222 KB
Volume
132
Category
Article
ISSN
0022-314X

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πŸ“œ SIMILAR VOLUMES

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Canonical number systems are the natural generalization of q-adic number systems to number fields. Such number systems admit a certain representation of each algebraic integer of a given number field with respect to the powers of a given base number b. The aim of this paper is to study the sum of di

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Let Q=[Q j ] j=0 be a strictly increasing sequence of integers with Q 0 =1 and such that each Q j is a divisor of Q j+1 . The sequence Q is a numeration system in the sense that every positive integer n has a unique ``base-Q'' representation of the form n= j 0 a j (n) Q j with ``digits'' a j (n) sat

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The aim of this paper is to provide detailed estimates for the discrepancy of the sequences ([: } s q (n)]) ([x] denotes the fractional part of x) and results concerning the uniform distribution and the discrepancy of the sequences ([: 1 } s q 1 (n)], ..., [: d } s q d (n)]), where :, : 1 , ..., : d