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Distance formulae and invariant subspaces, with an application to localization of zeros of the Riemann $$\zeta$$-function. (English) Zbl 0816.30026
Summary: It is proved that a subspace of a holomorphic Hilbert space is completely determined by their distances to the reproducing kernels. A simple rule is established to localize common zeros of a subspace of the Hardy space of the unit disc. As an illustration we show a series of discs of the complex plane free of zeros of the Riemann $$\zeta$$-function.

##### MSC:
 30H10 Hardy spaces 46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) 11M06 $$\zeta (s)$$ and $$L(s, \chi)$$
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