Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Rarified sums of the Thue-Morse sequence
HTML articles powered by AMS MathViewer

by Michael Drmota and Mariusz Skałba PDF
Trans. Amer. Math. Soc. 352 (2000), 609-642 Request permission

Abstract:

Let $q$ be an odd number and $S_{q,0}(n)$ the difference between the number of $k<n$, $k\equiv 0\bmod q$, with an even binary digit sum and the corresponding number of $k<n$, $k\equiv 0\bmod q$, with an odd binary digit sum. A remarkable theorem of Newman says that $S_{3,0}(n)>0$ for all $n$. In this paper it is proved that the same assertion holds if $q$ is divisible by 3 or $q=4^N+1$. On the other hand, it is shown that the number of primes $q\le x$ with this property is $o(x/\log x)$. Finally, analoga for “higher parities” are provided.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 11B85, 11A63
  • Retrieve articles in all journals with MSC (1991): 11B85, 11A63
Additional Information
  • Michael Drmota
  • Affiliation: Department of Geometry, Technical University of Vienna, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria
  • MR Author ID: 59890
  • Email: michael.drmota@tuwien.ac.at
  • Mariusz Skałba
  • Affiliation: Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland
  • Email: skalba@mimuw.edu.pl
  • Received by editor(s): July 6, 1995
  • Received by editor(s) in revised form: December 2, 1997
  • Published electronically: August 10, 1999
  • Additional Notes: This work was supported by the Austrian Science Foundation, grant Nr. M 00233–MAT
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 352 (2000), 609-642
  • MSC (1991): Primary 11B85; Secondary 11A63
  • DOI: https://doi.org/10.1090/S0002-9947-99-02277-1
  • MathSciNet review: 1491859