Geodesic
Mean Values of Character Sums
Canadian journal of mathematics, Tome 31 (1979) no. 3, pp. 476-487

Voir la notice de l'article provenant de la source Cambridge University Press

For a non-principal Dirichlet character χ modulo q, Let the Pólya-Vingradov inequality asserts that M(x) < q 1/2 log q see [7]. in the opposite direction it is a trivial consequence of lemma 1 below and 1. Parseval's identity that if χ is primitive modulo q, then We show that on average the latter of these estimates is the more precise.THEOREM 1. For any real k > 0 where the summation is over all non-principal characters modulo q.THEOREM 2. For any k > 0, 
Montgomery, H. L.; Vaughan, R. C. Mean Values of Character Sums. Canadian journal of mathematics, Tome 31 (1979) no. 3, pp. 476-487. doi: 10.4153/CJM-1979-053-2
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