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March 2016 Multiples of squares in short intervals
Joël Rivat, Igor E. Shparlinski
Funct. Approx. Comment. Math. 54(1): 57-63 (March 2016). DOI: 10.7169/facm/2016.54.1.5

Abstract

We use the theory of exponent pairs and Vaaler polynomials to show that any interval of the form $[x,x+x^{1/2}]$ contains an integral multiple $m^2r \in [x,x+x^{1/2}]$ of a perfect square $m^2$ with an integer $m > x^{0.281286}$.

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Joël Rivat. Igor E. Shparlinski. "Multiples of squares in short intervals." Funct. Approx. Comment. Math. 54 (1) 57 - 63, March 2016. https://doi.org/10.7169/facm/2016.54.1.5

Information

Published: March 2016
First available in Project Euclid: 22 March 2016

zbMATH: 06862334
MathSciNet: MR3477734
Digital Object Identifier: 10.7169/facm/2016.54.1.5

Subjects:
Primary: 11N25

Keywords: exponential sums , multiples of squares , short intervals

Rights: Copyright © 2016 Adam Mickiewicz University

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Vol.54 • No. 1 • March 2016
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