Positive-density sets A and B in the integers satisfy d(A+B)=d(A)+d(B) precisely when they are not both contained in a proper finite union of residue classes.
The critical pairs of subsets of a group of prime order
3 Pith papers cite this work. Polarity classification is still indexing.
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A continuous φ: T → T satisfies φ(x) = w x + t with w integer if the A(T)-norm of exp(-2π i z φ) is O(log^{1/8-ε} |z|) as |z| → ∞.
Modular Schur numbers for linear equation systems depend only on the number of equations, independent of coefficients.
citing papers explorer
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An inverse theorem for sumsets of sets of positive density in the integers
Positive-density sets A and B in the integers satisfy d(A+B)=d(A)+d(B) precisely when they are not both contained in a proper finite union of residue classes.
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The quantitative Beurling-Helson Theorem
A continuous φ: T → T satisfies φ(x) = w x + t with w integer if the A(T)-norm of exp(-2π i z φ) is O(log^{1/8-ε} |z|) as |z| → ∞.
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Modular Schur numbers
Modular Schur numbers for linear equation systems depend only on the number of equations, independent of coefficients.