A major difficulty in trying to construct a proof of RH through analysis is that the zeros of L-functions behave so much differently from zeros of many of the s we are used to seeing in mathematics and mathematical physics. For example, it is known that the zeta-function does not satisfy any differential equation. The functions which do arise as solutions of some of the classical differential equations, such as s, s, etc., have zeros which are fairly regularly spaced. A similar remark holds for the zeros of solutions of classical differential equations regarded as a function of a parameter in the differential equation.
American mathematician
(born June 23, 1955) is an American mathematician, known for his research in analytic number theory, involving s, the , and questions related to the (RH). He was elected a Fellow of the in 2015.
From: Wikiquote (CC BY-SA 4.0)
Alternative Names:
J. Brian Conrey
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J. Conrey
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J. B. Conrey
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John Brian Conrey
From Wikidata (CC0)
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In 1972 announced a remarkable connection between the distribution of the zeros of the Riemann zeta-function and the distribution of eigenvalues of large random Hermitian matrices. Since then a number of startling developments have occurred making this connection more profound. In particular, random matrix theory has been found to be an extremely useful predictive tool in the theory of L-functions.