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Proceedings of the American Mathematical Society

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

 

 

Estimates for exponential sums


Author: Robert A. Smith
Journal: Proc. Amer. Math. Soc. 79 (1980), 365-368
MSC: Primary 10G10
DOI: https://doi.org/10.1090/S0002-9939-1980-0567973-5
MathSciNet review: 567973
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Abstract: If f is a polynomial over Z of degree $ n + 1$ with $ n \geqslant 1$, then for each integer $ q \geqslant 1,\vert{\Sigma _{1 \leqslant x \leqslant q}}\exp (2\pi if(x)/q)\vert \leqslant {q^{1/2}}(D,q){d_n}(q)$, provided the discriminant D of the derivative of f does not vanish identically, where $ {d_n}(q)$ is the number of representations of q as a product of n factors.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0567973-5
Article copyright: © Copyright 1980 American Mathematical Society