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Sum of Many Dilates

Part of: Sequences and sets Geometry of numbers Extremal combinatorics

Published online by Cambridge University Press:  08 September 2015

GEORGE SHAKAN
GEORGE SHAKAN*
Affiliation:
Department of Mathematics, University of Wyoming, Laramie, Wyoming 82072, USA (e-mail: [email protected])
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Abstract

We show that for any coprime integers λ1, . . ., λk and any finite A ⊂ $\mathbb{Z}$, one has

|\lambda_1 \cdot A + \cdots + \lambda_k \cdot A| \geq (|\lambda_1| + \cdots + |\lambda_k|)|A|- C,
where C only depends on λ1, . . ., λk.

MSC classification

Primary: 11B75: Other combinatorial number theory
Secondary: 11H99: None of the above, but in this section 05D99: None of the above, but in this section
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 25 , Issue 3 , May 2016 , pp. 460 - 469
Copyright
Copyright © Cambridge University Press 2015 

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