Trigonometric polynomials and lattice points

Authors:
J. Cilleruelo and A. Córdoba

Journal:
Proc. Amer. Math. Soc. **115** (1992), 899-905

MSC:
Primary 11P21

DOI:
https://doi.org/10.1090/S0002-9939-1992-1089403-8

MathSciNet review:
1089403

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Abstract | References | Similar Articles | Additional Information

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 , an arc whose length is smaller than contains, at most, lattice points. We use the same method to obtain sharp -estimates for uncompleted, Gaussian sums

**[1]**A. Zygmund,*A Cantor-Lebesgue theorem for double trigonometric series*, Studia Math.**64**(1972), 189-202. MR**0312149 (47:711)****[2]**G. H. Hardy and E. M. Wright,*Introduction to the theory of numbers*, 4th ed., Clarendon Press, Oxford, 1960.**[3]**W. B. Jurkat,*The proof of the central limit theorem for theta sums*, Duke Math. J.**48**(1981), 873-885. MR**782582 (86m:11059)****[4]**Z. Zalcwasser,*Sur les polynômes associes aux fonctions modulaires*, Studia Math.**7**(1937), 16-35.

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DOI:
https://doi.org/10.1090/S0002-9939-1992-1089403-8

Article copyright:
© Copyright 1992
American Mathematical Society