Distance formulae and invariant subspaces, with an application to localization of zeros of the Riemann $\zeta $-function

Nikolai Nikolski

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Displaying similar documents to “Distance formulae and invariant subspaces, with an application to localization of zeros of the Riemann $ζ$ -function”

Invariant subspaces on multiply connected domains.

Ali Abkar, Hakan Hedenmalm (1998)

Publicacions Matemàtiques

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The lattice of invariant subspaces of several Banach spaces of analytic functions on the unit disk, for example the Bergman spaces and the Dirichlet spaces, have been studied recently. A natural question is to what extent these investigations carry over to analogously defined spaces on an annulus. We consider this question in the context of general Banach spaces of analytic functions on finitely connected domains Ω. The main result reads as follows: Assume that B is a Banach space of...

The subspace theorem and applications.

Schlickewei, Hans Peter (1998)

Documenta Mathematica

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On the exact location of the non-trivial zeros of Riemann's zeta function

Juan Arias de Reyna, Jan van de Lune (2014)

Acta Arithmetica

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We introduce the real valued real analytic function κ(t) implicitly defined by $e^{2 π i κ (t)} = - e^{- 2 i ϑ (t)} (ζ^{'} (1 / 2 - i t)) / (ζ^{'} (1 / 2 + i t))$ (κ(0) = -1/2). By studying the equation κ(t) = n (without making any unproved hypotheses), we show that (and how) this function is closely related to the (exact) position of the zeros of Riemann’s ζ(s) and ζ’(s). Assuming the Riemann hypothesis and the simplicity of the zeros of ζ(s), it follows that the ordinate of the zero 1/2 + iγₙ of ζ(s) is the unique solution to the equation κ(t) = n.

An Asymptotic Formula for a sum Involving Zeros of the Riemann Zeta-function

Yuichi Kamiya, Masatoshi Suzuki (2004)

Publications de l'Institut Mathématique

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Large gaps between consecutive zeros of the Riemann zeta-function. II

H. M. Bui (2014)

Acta Arithmetica

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Assuming the Riemann Hypothesis we show that there exist infinitely many consecutive zeros of the Riemann zeta-function whose gaps are greater than 2.9 times the average spacing.

Two complete and minimal systems associated with the zeros of the Riemann zeta function

Jean-François Burnol (2004)

Journal de Théorie des Nombres de Bordeaux

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We link together three themes which had remained separated so far: the Hilbert space properties of the Riemann zeros, the “dual Poisson formula” of Duffin-Weinberger (also named by us co-Poisson formula), and the “Sonine spaces” of entire functions defined and studied by de Branges. We determine in which (extended) Sonine spaces the zeros define a complete, or minimal, system. We obtain some general results dealing with the distribution of the zeros of the de-Branges-Sonine entire functions....

Interior compact subspaces and differentiation in model subspaces.

Baranov, A.D. (2005)

Zapiski Nauchnykh Seminarov POMI

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Pair correlation of the zeros of the Riemann zeta function in longer ranges

Tsz Ho Chan (2004)

Acta Arithmetica

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On invariant subspaces for polynomially bounded operators

Junfeng Liu (2017)

Czechoslovak Mathematical Journal

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We discuss the invariant subspace problem of polynomially bounded operators on a Banach space and obtain an invariant subspace theorem for polynomially bounded operators. At the same time, we state two open problems, which are relative propositions of this invariant subspace theorem. By means of the two relative propositions (if they are true), together with the result of this paper and the result of C. Ambrozie and V. Müller (2004) one can obtain an important conclusion that every polynomially...

Corrections to “Radial limits in co-invariant subspaces"

D. R. Georgijević (1987)

Matematički Vesnik

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Counting distinct zeros of the Riemann zeta-function.

Farmer, David W. (1995)

The Electronic Journal of Combinatorics [electronic only]

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On the Linnik-Sprindžuk theorem about the zeros of L-functions

J. Kaczorowski, A. Perelli (2008)

Acta Arithmetica

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Displaying similar documents to “Distance formulae and invariant subspaces, with an application to localization of zeros of the Riemann ζ -function”

Displaying similar documents to “Distance formulae and invariant subspaces, with an application to localization of zeros of the Riemann $ζ$ -function”