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Zeros of combinations of the Riemann ξ-function on bounded vertical shifts


Dixit, Atul; Robles, Nicolas; Roy, Arindam; Zaharescu, Alexandru (2015). Zeros of combinations of the Riemann ξ-function on bounded vertical shifts. Journal of Number Theory, 149:404-434.

Abstract

In this paper we consider a series of bounded vertical shifts of the Riemann ξ-function. Interestingly, although such functions have essential singularities, infinitely many of their zeros lie on the critical line. We also generalize some integral identities associated with the theta transformation formula and some formulae of G.H. Hardy and W.L. Ferrar in the context of a pair of functions reciprocal in Fourier cosine transform.

Abstract

In this paper we consider a series of bounded vertical shifts of the Riemann ξ-function. Interestingly, although such functions have essential singularities, infinitely many of their zeros lie on the critical line. We also generalize some integral identities associated with the theta transformation formula and some formulae of G.H. Hardy and W.L. Ferrar in the context of a pair of functions reciprocal in Fourier cosine transform.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2015
Deposited On:27 Jan 2015 16:10
Last Modified:08 Dec 2017 10:33
Publisher:Elsevier
ISSN:0022-314X
Publisher DOI:https://doi.org/10.1016/j.jnt.2014.10.004

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