Header

UZH-Logo

Maintenance Infos

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.

Statistics

Citations

1 citation in Web of Science®
1 citation in Scopus®
Google Scholar™

Altmetrics

Downloads

0 downloads since deposited on 27 Jan 2015
0 downloads since 12 months

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:05 Apr 2016 18:51
Publisher:Elsevier
ISSN:0022-314X
Publisher DOI:https://doi.org/10.1016/j.jnt.2014.10.004

Download

Preview Icon on Download
Content: Published Version
Filetype: PDF - Registered users only
Size: 498kB
View at publisher

Article Networks

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations