Abstract
AbstractLet χ be a non-real Dirichlet character modulo a primeq. In this paper we prove that the distribution of the short character sumSχ,H(x)= ∑x<n≤x+Hχ(n), asxruns over the positive integers belowq, converges to a two-dimensional Gaussian distribution on the complex plane, provided that logH=o(logq) andH→ ∞ asq→ ∞. Furthermore, we use an idea of Selberg to establish an upper bound on the rate of convergence.
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