Skip to Main Content

Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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.

 

On the distribution of Kloosterman sums
HTML articles powered by AMS MathViewer

by Igor E. Shparlinski PDF
Proc. Amer. Math. Soc. 136 (2008), 419-425 Request permission

Abstract:

For a prime $p$, we consider Kloosterman sums \[ K_{p}(a) = \sum _{x\in \mathbb {F}_p^*} \exp (2 \pi i (x + ax^{-1})/p), \qquad a \in \mathbb {F}_p^*,\] over a finite field of $p$ elements. It is well known that due to results of Deligne, Katz and Sarnak, the distribution of the sums $K_{p}(a)$ when $a$ runs through $\mathbb {F}_p^*$ is in accordance with the Sato–Tate conjecture. Here we show that the same holds where $a$ runs through the sums $a = u+v$ for $u \in \mathcal {U}$, $v \in \mathcal {V}$ for any two sufficiently large sets $\mathcal {U}, \mathcal {V}\subseteq \mathbb {F}_p^*$. We also improve a recent bound on the nonlinearity of a Boolean function associated with the sequence of signs of Kloosterman sums.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11L05, 11L40, 11T71
  • Retrieve articles in all journals with MSC (2000): 11L05, 11L40, 11T71
Additional Information
  • Igor E. Shparlinski
  • Affiliation: Department of Computing, Macquarie University, Sydney, NSW 2109, Australia
  • MR Author ID: 192194
  • Email: igor@ics.mq.edu.au
  • Received by editor(s): August 20, 2006
  • Received by editor(s) in revised form: September 29, 2006
  • Published electronically: November 2, 2007
  • Additional Notes: During the preparation of this paper, the author was supported in part by ARC grant DP0556431.
  • Communicated by: Wen-Ching Winnie Li
  • © Copyright 2007 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 419-425
  • MSC (2000): Primary 11L05, 11L40, 11T71
  • DOI: https://doi.org/10.1090/S0002-9939-07-08943-5
  • MathSciNet review: 2358479