摘要

Let Omega(n) be the total number of prime factors of n and Theta(k)(x;q,a) = Sigma(n <= x) (Omega(n)=k) 1, where k is allowed to tend to infinity with respect to x. Combining the circle method with the Selberg Delange method, together with the result of Bombieri-type sum for exponential sums, we investigate the behavior of the error term of 0, (x; q, a) in the "mean" and obtain its upper bound.

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