Abstract
In a paper of Thuswaldner and Tichy, a version of Waring’s problem with restrictions on the sum of digits was considered. This paper is devoted to a generalization of their result to arbitrary completely q-additive functions.
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DELANGE, H.: Sur les fonctions q-additives ou q-multiplicatives, Acta Arith. 21 (1972), 285–298 (Errata insert).
FORD, K. B.: New estimates for mean values of Weyl sums, Int. Math. Res. Not. 3 (1995), 155–171 (Electronic).
KIM, D.-H.: On the joint distribution of q-additive functions in residue classes, J. Number Theory 74 (1999), 307–336.
NATHANSON, M. B.: Additive Number Theory. The Classical Bases. Grad. Texts in Math. 164, Springer-Verlag, New York, 1996.
PFEIFFER, O.— THUSWALDNER, J. M.: Waring’s problem restricted by a system of sum of digits congruences, Quaest. Math. 30 (2007), 513–523.
THUSWALDNER, J. M.— TICHY, R. F.: Waring’s problem with digital restrictions, Israel J. Math. 149 (2005), 317–344.
VAUGHAN, R. C.: The Hardy-Littlewood method (2nd ed.). Cambridge Tracts in Math. 125, Cambridge University Press, Cambridge, 1997.
VAUGHAN, R. C.— WOOLEY, T. D.: Waring’s problem: a survey. In: Number Theory for the Millennium, III (Urbana, IL, 2000), A. K. Peters, Natick, MA, 2002, pp. 301–340.
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(Communicated by Stanislav Jakubec)
This work was supported by Austrian Science Fund project no. S9611.
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Wagner, S. Waring’s problem with restrictions on q-additive functions. Math. Slovaca 59, 339–348 (2009). https://doi.org/10.2478/s12175-009-0130-7
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DOI: https://doi.org/10.2478/s12175-009-0130-7