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The Sum of Digits Function In Number Fields
Author(s) -
Thuswaldner Jörg M.
Publication year - 1998
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609397003731
Subject(s) - mathematics , function (biology) , quadratic equation , term (time) , function field , pure mathematics , mathematics subject classification , field (mathematics) , quantum mechanics , physics , geometry , evolutionary biology , biology
In this paper we are concerned with the asymptotic description of the sum of digits function of canonical number systems in number fields. We derive an asymptotic formula for its summatory function whose second term contains a periodic fluctuation. In imaginary quadratic fields this function is uniformly distributed with respect to the argument. 1991 Mathematics Subject Classification 11R04, 11H06.