On the Waring problem with Dickson polynomials in finite fields
Authors:
Alina Ostafe and Igor E. Shparlinski
Journal:
Proc. Amer. Math. Soc. 139 (2011), 38153820
MSC (2010):
Primary 11T06, 11T30
Published electronically:
March 11, 2011
MathSciNet review:
2823028
Fulltext PDF
Abstract 
References 
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Additional Information
Abstract: We improve recent results of D. Gomez and A. Winterhof on the Waring problem with Dickson polynomials in finite fields. Our approach is based on recent advances in arithmetic combinatorics in arbitrary finite fields due to A. Glibichuk and M. Rudnev.
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 W.S. Chou, G. L. Mullen and B. Wassermann, `On the number of solutions of equations of Dickson polynomials over finite fields', Taiwanese J. Math., 12 (2008), 917931. MR 2426536 (2009f:11148)
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 V. C. Garcia, `On the distribution of sparse sequences in prime fields and applications', preprint, 2010 (available from http://arxiv.org/abs/1008.4180).
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 V. C. Garcia, F. Luca and V. J. Mejia, `On sums of Fibonacci numbers modulo ', Bull. Aust. Math. Soc. (to appear).
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 A. Glibichuk, `Sums of powers of subsets of arbitrary finite fields', Izv. Ross. Akad. Nauk Ser. Mat. (transl. as Izvestiya. Mathematics), to appear (in Russian).
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 A. Winterhof and C. van de Woestijne, `Exact solutions to Waring's problem in finite fields', Acta Arith., 141 (2010), 171190. MR 2579843
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Additional Information
Alina Ostafe
Affiliation:
Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH8057, Zürich, Switzerland
Email:
alina.ostafe@math.uzh.ch
Igor E. Shparlinski
Affiliation:
Department of Computing, Macquarie University, Sydney, NSW 2109, Australia
Email:
igor.shparlinski@mq.edu.au
DOI:
http://dx.doi.org/10.1090/S000299392011108438
PII:
S 00029939(2011)108438
Received by editor(s):
September 12, 2010
Published electronically:
March 11, 2011
Additional Notes:
During the preparation of this paper, the first author was supported in part by SNF Grant 121874 (Switzerland) and the second author by ARC Grant DP1092835 (Australia) and by NRF Grant CRP2200703 (Singapore)
Communicated by:
Matthew A. Papanikolas
Article copyright:
© Copyright 2011
American Mathematical Society
