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Finite generating functions for the sum-of-digits sequence

  • Christophe Vignat
  • Tanay Wakhare
Article

Abstract

We derive some new finite sums involving the sequence \(s_{2}\left( n\right) ,\) the sum-of-digits of the expansion of n in base 2. These functions allow us to generalize some classical results obtained by Allouche, Shallit and others.

Keywords

Sum-of-digits Hurwitz zeta function Infinite products Lambert transform 

Notes

Acknowledgements

The authors thank Eric Rowland for interesting comments on an earlier version of this manuscript, and Terri, Sen, Valerio, Natalie, and the Calvert Suite for their support. This material is based upon work supported by the National Science Foundation under Grant No. DMS-1439786 while the first author was in residence at the Institute for Computational and Experimental Research in Mathematics in Providence, RI, during the Point Configurations in Geometry, Physics and Computer Science Semester Program.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.L.S.S., CentraleSupélecUniversité Paris SudOrsayFrance
  2. 2.Department of MathematicsTulane UniversityNew OrleansUSA
  3. 3.University of MarylandCollege ParkUSA

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