Small Solutions of Polynomial Congruences
نویسنده
چکیده
Let p be prime and q|p − 1. Suppose xq ≡ a(mod p) has a solution. We estimate the size of the smallest solution x0 with 0 < x0 < p. We prove that |x0| p3/2q−1 log p. By applying the Burgess character sum estimates, and estimates of certain exponential sums due to Bourgain, Glibichuk and Konyagin, we derive refinements of our result.
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تاریخ انتشار 2010