TY - JOUR
T1 - On the distribution of arguments of gauss sums
AU - Shparlinski, Igor E.
PY - 2009
Y1 - 2009
N2 - Let Fq 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. Where χ is a non-principal multiplicative character of the multiplicative group Fq* and Tr(z) is the trace of z ∈ Fq into Fp. 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 A and X of Fq* and the set of all multiplicative characters of Fq*, respectively.
AB - Let Fq 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. Where χ is a non-principal multiplicative character of the multiplicative group Fq* and Tr(z) is the trace of z ∈ Fq into Fp. 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 A and X of Fq* and the set of all multiplicative characters of Fq*, respectively.
UR - http://www.scopus.com/inward/record.url?scp=77956671268&partnerID=8YFLogxK
U2 - 10.2996/kmj/1238594554
DO - 10.2996/kmj/1238594554
M3 - Article
AN - SCOPUS:77956671268
SN - 0386-5991
VL - 32
SP - 172
EP - 177
JO - Kodai Mathematical Journal
JF - Kodai Mathematical Journal
IS - 1
ER -