Multiples of squares in short intervals

Joël Rivat; Igor E. Shparlinski

doi:10.7169/facm/2016.54.1.5

Multiples of squares in short intervals

Joël Rivat, Igor E. Shparlinski

Research output: Contribution to journal › Article › peer-review

Abstract

We use the theory of exponent pairs and Vaaler polynomials to show that any interval of the form [x; x+x₁₌₂] contains an integral multiple m²r ∈ [x; x+x₁₌₂] of a perfect square m² with an integer m > x^0:281286.

Original language	English
Pages (from-to)	57-63
Number of pages	7
Journal	Functiones et Approximatio, Commentarii Mathematici
Volume	54
Issue number	1
DOIs	https://doi.org/10.7169/facm/2016.54.1.5
Publication status	Published - 2016
Externally published	Yes

Keywords

Exponential sums
Multiples of squares
Short intervals

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10.7169/facm/2016.54.1.5

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abstract = "We use the theory of exponent pairs and Vaaler polynomials to show that any interval of the form [x; x+x1=2] contains an integral multiple m2r ∈ [x; x+x1=2] of a perfect square m2 with an integer m > x0:281286.",

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AB - We use the theory of exponent pairs and Vaaler polynomials to show that any interval of the form [x; x+x1=2] contains an integral multiple m2r ∈ [x; x+x1=2] of a perfect square m2 with an integer m > x0:281286.

KW - Exponential sums

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Multiples of squares in short intervals

Abstract

Keywords

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