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Hildebrand, A.J. Hoit, Abigail 2015-09-28T15:20:26Z 2015-09-28T15:20:26Z 10000-01-01 1999 1999 "Let Q=Qjinfinity j=0 be a strictly increasing sequence of integers with Q 0 = 1 and such that each Qj is a divisor of Qj+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≥0aj nQj with ""digits"" aj( n) satisfying 0≤ajn<Q j+1/Qj . A Q-additive function is a function f:N→ C of the form fn=j≥ 0fjaj n where n=j≥0aj nQj is the base-Q representation of n and the component functions fj are defined on 0,1,&ldots;, Qj+1/Qj-1 and satisfy fj(0) = 0. These functions generalize the sum-of-digits functions for base-Q representations, defined by sQn= j≥0ajn . We consider the distribution of integer-valued Q-additive functions in residue classes modulo a prime m and also the distribution of real-valued Q-additive functions modulo 1. In each case, we give necessary and sufficient conditions for a Q -additive function to be uniformly (resp. non-uniformly) distributed. We also introduce so-called block product sequences, which are sequences obtained by a certain algebraic operation on finite blocks of digits, and show that these sequences are closely related to Q-additive functions." Made available in DSpace on 2015-09-28T15:20:26Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 9944880.pdf: 2640909 bytes, checksum: a5a9dc5eda8485c484b31ad425f07ffe (MD5) Previous issue date: 1999 Embargo set by: Seth Robbins for item 88256 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 62 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1999. http://hdl.handle.net/2142/86975 (MiAaPQ)AAI9944880 eng Mathematics The Distribution of Generalized Sum -of -Digits Functions text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.