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The Sum of Digits Function in Number Fields: Distribution in Residue Classes

✍ Scribed by Jörg M Thuswaldner

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
153 KB
Volume
74
Category
Article
ISSN
0022-314X

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✦ Synopsis

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 digits function & b (#) of these number systems. In particular, we prove, that & b (#) is equidistributed in residue classes modulo m in any ideal s. Furthermore, we investigate the sum of digits function over sumsets.

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