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The sum of digits function in finite fields


Authors: Cécile Dartyge and András Sárközy
Journal: Proc. Amer. Math. Soc. 141 (2013), 4119-4124
MSC (2010): Primary 11A63; Secondary 11L99
DOI: https://doi.org/10.1090/S0002-9939-2013-11801-0
Published electronically: August 8, 2013
MathSciNet review: 3105855
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Abstract: We define and study certain sum of digits functions in the context of finite fields. We give the number of polynomial values of $ \mathbb{F}_q$ with a fixed sum of digits. We also state a result for the sum of digits of polynomial values with generator arguments.


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Additional Information

Cécile Dartyge
Affiliation: Institut Élie Cartan, Université de Lorraine, BP 239, 54506 Vandœuvre Cedex, France
Email: Cecile.Dartyge@univ-lorraine.fr

András Sárközy
Affiliation: Department of Algebra and Number Theory, Eötvös Loránd University, 1117 Budapest, Pázmány Péter sétány 1/C, Hungary
Email: sarkozy@cs.elte.hu

DOI: https://doi.org/10.1090/S0002-9939-2013-11801-0
Keywords: Sum of digits function, finite fields, character sums, generators, primitive elements
Received by editor(s): February 2, 2012
Published electronically: August 8, 2013
Additional Notes: The research of the first author was partially supported by the Agence Nationale de la Recherche, grant ANR-10-BLAN 0103 MUNUM
The research of the second author was partially supported by the Hungarian National Foundation for Scientific Research, grants K72731 and K100291.
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2013 American Mathematical Society

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