Exact Kronecker constants of Hadamard sets

Tom 130 / 2013

Kathryn E. Hare, L. Thomas Ramsey 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.
    Canada, N2L 3G1
    e-mail
  • L. Thomas RamseyDepartment of Mathematics
    University of Hawaii at Manoa
    Honolulu, HI 96822, U.S.A.
    e-mail

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