On the distribution of arguments of Gauss sums

Shparlinski, Igor E.

Kodai Math. J., Tome 32 (2009) no. 1, p. 172-177 / Harvested from Project Euclid

Résumé

Let F_q be a finite field of q elements of characteristic p. N. M. Katz and Z. Zheng have shown the uniformity of distribution of the arguments arg G (a, χ) of all (q - 1)(q - 2) nontrivial Gauss sums ¶ $G(a, \chi) = \sum_{x \in {\mathbf F}_q} \chi(x) \exp(2 \pi i \mathrm{Tr}(ax)/p),$ ¶ where χ is a non-principal multiplicative character of the multiplicative group F_q^* and Tr(z) is the trace of z $\in$ F_q into F_p. ¶ Here we obtain a similar result for the set of arguments arg G(a, χ) when a and χ run through arbitrary (but sufficiently large) subsets ${\mathcal A}$ and ${\mathcal X}$ of F_q^* and the set of all multiplicative characters of F_q^*, respectively.

Publié le : 2009-03-15
Classification:

@article{1238594554,
     author = {Shparlinski, Igor E.},
     title = {On the distribution of arguments of Gauss sums},
     journal = {Kodai Math. J.},
     volume = {32},
     number = {1},
     year = {2009},
     pages = { 172-177},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1238594554}
}

Shparlinski, Igor E. On the distribution of arguments of Gauss sums. Kodai Math. J., Tome 32 (2009) no. 1, pp.  172-177. http://gdmltest.u-ga.fr/item/1238594554/