Chapter

Sequences and Their Applications – SETA 2010

Volume 6338 of the series Lecture Notes in Computer Science pp 196-203

Ternary Kloosterman Sums Modulo 18 Using Stickelberger’s Theorem

  • Faruk GöloğluAffiliated withSchool of Mathematical Sciences, University College Dublin
  • , Gary McGuireAffiliated withSchool of Mathematical Sciences, University College Dublin
  • , Richard MoloneyAffiliated withSchool of Mathematical Sciences, University College Dublin

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Abstract

A result due to Helleseth and Zinoviev characterises binary Kloosterman sums modulo 8. We give a similar result for ternary Kloosterman sums modulo 9. This leads to a complete characterisation of values that ternary Kloosterman sums assume modulo 18. The proof uses Stickelberger’s theorem and Fourier analysis.

Keywords

Kloosterman sums Stickelberger’s theorem