Publication: Zeros of combinations of the Riemann ξ-function on bounded vertical shifts
Zeros of combinations of the Riemann ξ-function on bounded vertical shifts
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Dixit, A., Robles, N., Roy, A., & Zaharescu, A. (2015). Zeros of combinations of the Riemann ξ-function on bounded vertical shifts. Journal of Number Theory, 149, 404–434. https://doi.org/10.1016/j.jnt.2014.10.004
Abstract
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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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- Dixit, Atul
- Robles, Nicolas
- Roy, Arindam
- Zaharescu, Alexandru
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Dixit, A., Robles, N., Roy, A., & Zaharescu, A. (2015). Zeros of combinations of the Riemann ξ-function on bounded vertical shifts. Journal of Number Theory, 149, 404–434. https://doi.org/10.1016/j.jnt.2014.10.004
