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On the Baez-Duarte Approach to the Nyman-Beaurling Criterion for the Riemann Hypothesis

Juncos, Daniel Mario (2011) On the Baez-Duarte Approach to the Nyman-Beaurling Criterion for the Riemann Hypothesis. Master's Thesis, University of Pittsburgh.

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    Abstract

    The Nyman-Beurling Criterion paraphrases the Riemann Hypothesis as a closure problem in a Hilbert space. The simplest version of this, due to Baez-Duarte, states that RH is equivalent to one particular element in a Hilbert space being in the closure of a span of countably many other elements. We investigate this numerically and analytically. In particular, we establish new formulas for the inner products of the vectors involved.


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    Item Type: University of Pittsburgh ETD
    Creators/Authors:
    CreatorsEmailORCID
    Juncos, Daniel Mariodmj18@pitt.edu
    ETD Committee:
    ETD Committee TypeCommittee MemberEmailORCID
    Committee ChairBorisov, Alexanderborisov@pitt.edu
    Committee MemberWheeler, Jeffreyjwheeler@pitt.edu
    Committee MemberKaveh, Kiumarskaveh@pitt.edu
    Title: On the Baez-Duarte Approach to the Nyman-Beaurling Criterion for the Riemann Hypothesis
    Status: Unpublished
    Abstract: The Nyman-Beurling Criterion paraphrases the Riemann Hypothesis as a closure problem in a Hilbert space. The simplest version of this, due to Baez-Duarte, states that RH is equivalent to one particular element in a Hilbert space being in the closure of a span of countably many other elements. We investigate this numerically and analytically. In particular, we establish new formulas for the inner products of the vectors involved.
    Date: 06 June 2011
    Date Type: Completion
    Defense Date: 21 April 2011
    Approval Date: 06 June 2011
    Submission Date: 22 April 2011
    Access Restriction: 5 year -- Restrict access to University of Pittsburgh for a period of 5 years.
    Patent pending: No
    Institution: University of Pittsburgh
    Thesis Type: Master's Thesis
    Refereed: Yes
    Degree: MS - Master of Science
    URN: etd-04222011-135102
    Uncontrolled Keywords: Baez-Duarte; Riemann Hypothesis
    Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
    Date Deposited: 10 Nov 2011 14:41
    Last Modified: 30 May 2012 14:01
    Other ID: http://etd.library.pitt.edu/ETD/available/etd-04222011-135102/, etd-04222011-135102

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