Article
Exponential Sums With Polynomial Values of the Discrete Logarithm
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Abstract
We estimate exponential sums of the formf(ind n) exp 2πi , p − 1 M+1nM+N where f is a polynomial with integer coefficients, and ind n is the discrete loga- rithm of n modulo an odd prime p and a primitive root g. We apply this estimate to show that the values ind n, . . . , (ind n)m, M + 1nM + N, are uniformly and independently distributed modulo p − 1.
Keywords
Discrete logarithm, primitive root, index, uniform distribution.
Citation
Banks, W. D. & Shparlinski, I. E. (2007). Exponential sums with polynomial values of the discrete logarithm. Uniform Distribution Theory, 2(2), 67–72.
W. D. Banks and I. E. Shparlinski, “Exponential sums with polynomial values of the discrete logarithm,” Uniform Distribution Theory, vol. 2, no. 2, pp. 67–72, 2007.
Banks WD, Shparlinski IE. Exponential sums with polynomial values of the discrete logarithm. Uniform Distribution Theory. 2007;2(2):67–72.
Banks, W. D. and Shparlinski, I. E. (2007), ‘Exponential sums with polynomial values of the discrete logarithm’, Uniform Distribution Theory, 2(2), pp. 67–72.
Banks, William D., and Igor E. Shparlinski. “Exponential Sums with Polynomial Values of the Discrete Logarithm.” Uniform Distribution Theory, vol. 2, no. 2, 2007, pp. 67–72.
Banks, William D., and Igor E. Shparlinski. “Exponential Sums with Polynomial Values of the Discrete Logarithm.” Uniform Distribution Theory 2, no. 2 (2007): 67–72.
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Published by: Engineering Journals
