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The Sum‐of‐Digits Function for Complex Bases
Author(s) -
Grabner Peter J.,
Kirschenhofer Peter,
Prodinger Helmut
Publication year - 1998
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610798005663
Subject(s) - function (biology) , mathematics , integer (computer science) , argument (complex analysis) , combinatorics , discrete mathematics , pure mathematics , computer science , evolutionary biology , programming language , biochemistry , chemistry , biology
We consider digital expansions with respect to complex integer bases. We derive precise information about the length of these expansions and the corresponding sum‐of‐digits function. Furthermore we give an asymptotic formula for the sum‐of‐digits function in large circles and prove that this function is uniformly distributed with respect to the argument. Finally the summatory function of the sum‐of‐digits function along the real axis is analyzed.