On the Barban-Davenport Halberstam theorem: XIXArticle

• 1 University of Whales

The present paper deals with the dispersion

$$G(x,Q)=\sum_{k\leq Q}\sum_{0<a\leq k}\{S(x;a,k)-f(a,k)x\}^2$$ for large $Q$, and improves the lower bound by proving that $G(x,Q)>\frac{1}{12}\{\Gamma(C)+o(1)\}Q^2+O(x \log_{-A}x)$ when $x/Q\rightarrow\infty$ where $\Gamma(C)$ is an explicitly defined function of $C$.

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