# 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.

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.

## Citations

1 citation in Web of Science®
1 citation in Scopus®

## Altmetrics

Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English 2015 27 Jan 2015 16:10 05 Apr 2016 18:51 Elsevier 0022-314X https://doi.org/10.1016/j.jnt.2014.10.004
Permanent URL: https://doi.org/10.5167/uzh-105426