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Creators/Authors contains: "Lim, Jeck"

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  1. ; (, Advances in Mathematics)
    Free, publicly-accessible full text available November 1, 2026
  2. ; (, Transactions of the American Mathematical Society)
    We show that if L 1 \mathcal {L}_1 and L 2 \mathcal {L}_2 are linear transformations from Z d \mathbb {Z}^d to Z d \mathbb {Z}^d satisfying certain mild conditions, then, for any finite subset A A of Z d \mathbb {Z}^d , | L 1 A + L 2 A | ≥<#comment/> ( | det ( L 1 ) | 1 / d + | det ( L 2 ) | 1 / d ) d | A | −<#comment/> o ( | A | ) . \begin{equation*} |\mathcal {L}_1 A+\mathcal {L}_2 A|\geq \left ( |\det (\mathcal {L}_1)|^{1/d}+|\det (\mathcal {L}_2)|^{1/d} \right )^d|A|- o(|A|). \end{equation*} This result corrects and confirms the two-summand case of a conjecture of Bukh and is best possible up to the lower-order term for certain choices of L 1 \mathcal {L}_1 and L 2 \mathcal {L}_2 . As an application, we prove a lower bound for | A + λ<#comment/> ⋅<#comment/> A | |A + \lambda \cdot A| when A A is a finite set of real numbers and λ<#comment/> \lambda is an algebraic number. In particular, when λ<#comment/> \lambda is of the form ( p / q ) 1 / d (p/q)^{1/d} for some p , q , d ∈<#comment/> N p, q, d \in \mathbb {N} , each taken as small as possible for such a representation, we show that | A + λ<#comment/> ⋅<#comment/> A | ≥<#comment/> ( p 1 / d + q 1 / d ) d | A | −<#comment/> o ( | A | ) . \begin{equation*} |A + \lambda \cdot A| \geq (p^{1/d} + q^{1/d})^d |A| - o(|A|). \end{equation*} This is again best possible up to the lower-order term and extends a recent result of Krachun and Petrov which treated the case λ<#comment/> = 2 \lambda = \sqrt {2} . 
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    Free, publicly-accessible full text available July 31, 2026
  3. ; (, Israel Journal of Mathematics)
    Free, publicly-accessible full text available June 1, 2026
  4. ; (, Discrete & Computational Geometry)
    Full Text Available 
  5. ; (, Bulletin of the London Mathematical Society)
    Abstract We show that there is an absolute constant such that for any finite subset of and any transcendental number . By a construction of Konyagin and Łaba, this is best possible up to the constant . 
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