caa a22 4500 463177886 CHVBK 20180406164830.0 cr unu---uuuuu 170326e20070801xx s 000 0 eng 10.1007/s11139-006-0001-6 doi (NATIONALLICENCE)springer-10.1007/s11139-006-0001-6 Wagner Stephan Department of Mathematics, Graz University of Technology, Steyrergasse 30, A-8010, Graz, Austria aut Numbers with fixed sum of digits in linear recurrent number systems [Elektronische Daten] [Stephan Wagner] We study the set of integers with a given sum of digits with respect to a linear recurrent digit system. An asymptotic formula for the number of integers ≤N with given sum of digits is determined, and the distribution in residue classes is investigated, thus generalizing results due to Mauduit and Sárközy. It turns out that numbers with fixed sum of digits are uniformly distributed in residue classes under some very general conditions. Namely, the underlying linear recurring sequence must have the property that there is no prime factor P of the modulus such that all but finitely many members of the sequence leave the same residue modulo P. The key step in the proof is an estimate for exponential sums using known theorems from Diophantine approximation. Springer Science + Business Media, LLC, 2006 Linear recurrent digit system nationallicence Sum of digits nationallicence Residue distribution nationallicence The Ramanujan Journal Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 14/1(2007-08-01), 43-68 1382-4090 14:1<43 2007 14 11139 https://doi.org/10.1007/s11139-006-0001-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11139-006-0001-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Wagner Stephan Department of Mathematics, Graz University of Technology, Steyrergasse 30, A-8010, Graz, Austria aut NATIONALLICENCE 773 0- The Ramanujan Journal Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 14/1(2007-08-01), 43-68 1382-4090 14:1<43 2007 14 11139 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer