On the distribution of Kloosterman sums
| dc.creator | Shparlinski, I. E. | |
| dc.date | 2006-08-24 | |
| dc.date.accessioned | 2026-07-07T07:22:06Z | |
| dc.date.available | 2026-07-07T07:22:06Z | |
| dc.description | For a prime $p$, we consider Kloosterman sums $$ K_{p}(a) = \sum_{x\in \F_p^*} \exp(2 πi (x + ax^{-1})/p), \qquad a \in \F_p^*, $$ 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 $\F_p^*$ 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 $u \in \cU$, $v \in \cV$ for any two sufficiently large sets $\cU, \cV \subseteq \F_p^*$. We also improve a recent bound on the nonlinearity of a Boolean function associated with the sequence of signs of Kloosterman sums. | |
| dc.identifier | https://arxiv.org/abs/math/0608595 | |
| dc.identifier | http://arxiv.org/abs/math/0608595 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115540 | |
| dc.subject | Number Theory | |
| dc.subject | 11L05, 11L26 | |
| dc.title | On the distribution of Kloosterman sums | |
| dc.type | text |