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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Trigonometric polynomials and lattice points


Authors: J. Cilleruelo and A. Córdoba
Journal: Proc. Amer. Math. Soc. 115 (1992), 899-905
MSC: Primary 11P21
MathSciNet review: 1089403
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Abstract: In this paper we study the distribution of lattice points on arcs of circles centered at the origin. We show that on such a circle of radius $ R$, an arc whose length is smaller than $ \sqrt 2 {R^{1/2 - 1(4[m/2] + 2)}}$ contains, at most, $ m$ lattice points. We use the same method to obtain sharp $ {L^4}$-estimates for uncompleted, Gaussian sums


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DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1089403-8
PII: S 0002-9939(1992)1089403-8
Article copyright: © Copyright 1992 American Mathematical Society