Roots of the derivative of the Riemann zeta function and of characteristic polynomials
| Autor: | David W. Farmer, C. P. Hughes, Eduardo Dueñez, Toan Phan, Sara Froehlich, Francesco Mezzadri |
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| Rok vydání: | 2010 |
| Předmět: |
Pure mathematics
Conjecture Distribution (number theory) Mathematics - Number Theory 11M50 15B52 Applied Mathematics General Physics and Astronomy Order (ring theory) FOS: Physical sciences Statistical and Nonlinear Physics Derivative Unitary matrix Mathematical Physics (math-ph) Riemann zeta function symbols.namesake symbols FOS: Mathematics Number Theory (math.NT) Random matrix Mathematical Physics Characteristic polynomial Mathematics |
| DOI: | 10.48550/arxiv.1002.0372 |
| Popis: | We investigate the horizontal distribution of zeros of the derivative of the Riemann zeta function and compare this to the radial distribution of zeros of the derivative of the characteristic polynomial of a random unitary matrix. Both cases show a surprising bimodal distribution which has yet to be explained. We show by example that the bimodality is a general phenomenon. For the unitary matrix case we prove a conjecture of Mezzadri concerning the leading order behavior, and we show that the same follows from the random matrix conjectures for the zeros of the zeta function. Comment: 24 pages, 6 figures |
| Databáze: | OpenAIRE |
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