The Smoothed Pólya–Vinogradov Inequality
نویسندگان
چکیده
Let χ be a primitive Dirichlet character to the modulus q. Let Sχ(M,N) = ∑ M 3, there is a primitive root g and an integer x ∈ [1, p − 1] such that g ≡ x mod p. It has also been used to improve the best known numerically explicit upper bound on the least inert prime in a real quadratic field. In this paper we will prove a smoothed Pólya–Vinogradov inequality which takes into account the arithmetic properties of the modulus and we extend the inequality to imprimitive characters. We also find a lower bound for the inequality.
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