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On the Constant in the Pólya-Vinogradov Inequality

Published online by Cambridge University Press:  20 November 2018

Adolf Hildebrand
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Abstract

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The Pólya-Vinogradov inequality states that for any non-principal character x modulo q and any N ≧ 1,

where c is an absolute constant. We show that (*) holds with c = 2/(3π2) + o(1) in the case x is primitive and x (— 1) =1 with c = 1/(3π) + o(l) in the case x is primitive and x(— 1) = — 1- This improves by a factor 2/3 the previously best-known values for these constants.

Keywords

10G15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 3 , 01 September 1988 , pp. 347 - 352
Copyright
Copyright © Canadian Mathematical Society 1988

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