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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An upper bound for the sum $\sum ^ {a+H}_ {n=a+1}f(n)$ for a certain class of functions $f$
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by Edward Dobrowolski and Kenneth S. Williams PDF
Proc. Amer. Math. Soc. 114 (1992), 29-35 Request permission

Abstract:

For a certain class of functions $f:Z \to C$ an upper bound is obtained for the sum $\sum \nolimits _{n = a + 1}^{a + H} {f\left ( n \right )}$. This bound is used to give a proof of a classical inequality due to Pólya and Vinogradov that does not require the value of the modulus of the Gauss sum and to obtain an estimate of the sum of Legendre symbols $\sum \nolimits _{x = 1}^H {( ( {R{g^x} + S} )/p} )$, where $g$ is a primitive root of the odd prime $p,1 \leq H \leq p - 1$ and $RS$ is not divisible by $p$.
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 114 (1992), 29-35
  • MSC: Primary 11L40
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1068118-6
  • MathSciNet review: 1068118