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Gulas, Master's Thesis-1.pdf (518.68 KB)

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Using Hilbert Space Theory and Quantum Mechanics to Examine the Zeros of The Riemann-Zeta Function

Gulas, Michael Allen
http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1594035551136634

Abstract Details

2020, Master of Arts (MA), Bowling Green State University, Mathematics.
In this thesis, I examine Hilbert Space Theory and the basic postulates of quantum mechanics and use these two different areas to look for zeros of the Riemann Zeta function. In particular, after stating some preliminaries of Hilbert Space Theory, I will examine how these ideas appear in quantum theory. As an illustrative example, I place a particle in the famous infinite square well to see these ideas in action. Finally, having discussed and explored quantum mechanics I will expound on the Riemann Zeta Function and the Riemann Hypothesis. I will then discuss various conjectures, that are a potential way to solve the famous Riemann Hypothesis via an unknown Hermitian operator on an unknown space. As Hamiltonian operators are Hermitian operators, we have a bridge into physics to take advantage of in solving this problem.
Kit Chan (Advisor)
So-Hsiang Chou (Committee Member)
60 p.
Mathematics; Physics; Quantum Physics
Hilbert Space Theory; Quantum Mechanics; Riemann Zeta; mathematics; physics; Riemann Hypothesis

Recommended Citations

Citations

  • Gulas, M. A. (2020). Using Hilbert Space Theory and Quantum Mechanics to Examine the Zeros of The Riemann-Zeta Function [Master's thesis, Bowling Green State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1594035551136634

    APA Style (7th edition)

  • Gulas, Michael. Using Hilbert Space Theory and Quantum Mechanics to Examine the Zeros of The Riemann-Zeta Function. 2020. Bowling Green State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1594035551136634.

    MLA Style (8th edition)

  • Gulas, Michael. "Using Hilbert Space Theory and Quantum Mechanics to Examine the Zeros of The Riemann-Zeta Function." Master's thesis, Bowling Green State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1594035551136634

    Chicago Manual of Style (17th edition)

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This open access ETD is published by Bowling Green State University and OhioLINK.