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## Exact Kronecker constants of Hadamard sets

### Tom 130 / 2013

Colloquium Mathematicum 130 (2013), 39-49 MSC: Primary 42A15, 43A46; Secondary 65T40. DOI: 10.4064/cm130-1-4

#### Streszczenie

A set $S$ of integers is called $\varepsilon$-Kronecker if every function on $S$ of modulus one can be approximated uniformly to within $\varepsilon$ by a character$.$ The least such $\varepsilon$ is called the $\varepsilon$-Kronecker constant, $\kappa(S)$. The angular Kronecker constant is the unique real number $\alpha(S)\in [0,1/2]$ such that $\kappa(S)=| \!\exp(2\pi i\alpha(S))-1 |.$ We show that for integers $m>1$ and $d \ge 1$, $$\alpha\{1,m,\ldots,m^{d-1}\}=\frac{m^{d-1}-1}{2(m^d-1)}\quad \text{and}\quad \alpha\{1,m,m^2,\ldots\}=1/(2m).$$

#### Autorzy

• Kathryn E. HareDepartment of Pure Mathematics
University of Waterloo
Waterloo, Ont.
e-mail
• L. Thomas RamseyDepartment of Mathematics
University of Hawaii at Manoa
Honolulu, HI 96822, U.S.A.
e-mail

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