location:  Publications → journals
Search results

Search: MSC category 11T24 ( Other character sums and Gauss sums )

 Expand all        Collapse all Results 1 - 4 of 4

1. CMB 2015 (vol 58 pp. 774)

Hanson, Brandon
 Character Sums over Bohr Sets We prove character sum estimates for additive Bohr subsets modulo a prime. These estimates are analogous to classical character sum bounds of PÃ³lya-Vinogradov and Burgess. These estimates are applied to obtain results on recurrence mod $p$ by special elements. Keywords:character sums, Bohr sets, finite fieldsCategories:11L40, 11T24, 11T23

2. CMB 2007 (vol 50 pp. 71)

Gurak, S.
 Polynomials for Kloosterman Sums Fix an integer $m>1$, and set $\zeta_{m}=\exp(2\pi i/m)$. Let ${\bar x}$ denote the multiplicative inverse of $x$ modulo $m$. The Kloosterman sums $R(d)=\sum_{x} \zeta_{m}^{x + d{\bar x}}$, $1 \leq d \leq m$, $(d,m)=1$, satisfy the polynomial $$f_{m}(x) = \prod_{d} (x-R(d)) = x^{\phi(m)} +c_{1} x^{\phi(m)-1} + \dots + c_{\phi(m)},$$ where the sum and product are taken over a complete system of reduced residues modulo $m$. Here we give a natural factorization of $f_{m}(x)$, namely, $$f_{m}(x) = \prod_{\sigma} f_{m}^{(\sigma)}(x),$$ where $\sigma$ runs through the square classes of the group ${\bf Z}_{m}^{*}$ of reduced residues modulo $m$. Questions concerning the explicit determination of the factors $f_{m}^{(\sigma)}(x)$ (or at least their beginning coefficients), their reducibility over the rational field ${\bf Q}$ and duplication among the factors are studied. The treatment is similar to what has been done for period polynomials for finite fields. Categories:11L05, 11T24

3. CMB 2003 (vol 46 pp. 344)

Gurak, S.
 Gauss and Eisenstein Sums of Order Twelve Let $q=p^{r}$ with $p$ an odd prime, and $\mathbf{F}_{q}$ denote the finite field of $q$ elements. Let $\Tr\colon\mathbf{F}_{q} \to\mathbf{F}_{p}$ be the usual trace map and set $\zeta_{p} =\exp(2\pi i/p)$. For any positive integer $e$, define the (modified) Gauss sum $g_{r}(e)$ by $$g_{r}(e) =\sum_{x\in \mathbf{F}_{q}}\zeta_{p}^{\Tr x^{e}}$$ Recently, Evans gave an elegant determination of $g_{1}(12)$ in terms of $g_{1}(3)$, $g_{1}(4)$ and $g_{1}(6)$ which resolved a sign ambiguity present in a previous evaluation. Here I generalize Evans' result to give a complete determination of the sum $g_{r}(12)$. Categories:11L05, 11T24

4. CMB 2001 (vol 44 pp. 22)

Evans, Ronald
 Gauss Sums of Orders Six and Twelve Precise, elegant evaluations are given for Gauss sums of orders six and twelve. Categories:11L05, 11T24
 top of page | contact us | privacy | site map |