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The distribution of short character sums
Published online by Cambridge University Press: 17 May 2013
Abstract
Let χ be a non-real Dirichlet character modulo a prime q. In this paper we prove that the distribution of the short character sum Sχ,H(x) = ∑x<n≤x+H χ(n), as x runs over the positive integers below q, converges to a two-dimensional Gaussian distribution on the complex plane, provided that log H=o(log q) and H → ∞ as q → ∞. Furthermore, we use an idea of Selberg to establish an upper bound on the rate of convergence.
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- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 155 , Issue 2 , September 2013 , pp. 207 - 218
- Copyright
- Copyright © Cambridge Philosophical Society 2013
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