Moisio型指数和计算

Evalutions on Moisio’s type exponential sums

本文计算一类Moisio型指数和.设2模r^(m)的阶为(r-1)/2·r^(m-1),其中r为奇素数, r≡1 (mod 4),m为正整数.设q=2((r-1)/2·r^(m-1)), Fq为q元有限域,χ为Fq到复数的经典加法特征.本文将给出指数和S(a, b)=∑x∈Fqχ(ax(q-1)/rm+bx)(a, b∈Fq)的值.特别地,本文运用有限域上椭圆曲线的有理点,计算一类S(a)=r^(m)/(q-1)S(a, 0)的值.

In this paper, we compute evaluations on a class of Moisio’s type exponential sums. Let 2 be of order (r-1)/2· r^(n-1) modulo 2^(m),where r is an odd prime, r ≡ 1(mod 4), and m is a positive integer. Let q=2((r-1)/2·r^(m-1)), Fq be the finite field with q elements, and χ be the canonical additive character from Fq to the complex number field.We shall give evaluations of exponential sums S(a, b)=∑x∈Fqχ(ax(q-1)/rm+bx),a, b∈Fq. Specially, we use the rational points of an elliptic curve over a finite field to compute evaluations of exponential sums S(a)=r^(m)/(q-1)S(a, 0).