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Bohr Cluster Points of Sidon Sets

L. Ramsey — 1995

Colloquium Mathematicae

It is a long standing open problem whether Sidon subsets of ℤ can be dense in the Bohr compactification of ℤ ([LR]). Yitzhak Katznelson came closest to resolving the issue with a random process in which almost all sets were Sidon and and almost all sets failed to be dense in the Bohr compactification [K]. This note, which does not resolve this open problem, supplies additional evidence that the problem is delicate: it is proved here that if one has a Sidon set which clusters at even one member of...

Exact Kronecker constants of Hadamard sets

Kathryn E. Hare;  L. Thomas Ramsey — 2013

Colloquium Mathematicae

A set S of integers is called ε-Kronecker if every function on S of modulus one can be approximated uniformly to within ε by a character. The least such ε is called the ε-Kronecker constant, κ(S). The angular Kronecker constant is the unique real number α(S) ∈ [0,1/2] such that κ(S) = |exp(2πiα(S)) - 1|. We show that for integers m > 1 and d ≥ 1, α 1 , m , . . . , m d - 1 = ( m d - 1 - 1 ) / ( 2 ( m d - 1 ) ) and α1,m,m²,... = 1/(2m).

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