Zeros of combinations of the Riemann Ξ-function and the confluent hypergeometric function on bounded vertical shifts

Show simple item record

dc.contributor.author Dixit, Atul
dc.contributor.author Kumar, Rahul
dc.contributor.author Maji, Bibekananda
dc.date.accessioned 2018-06-19T10:44:37Z
dc.date.available 2018-06-19T10:44:37Z
dc.date.issued 2018-06
dc.identifier.citation Dixit, Atul; Kumar, Rahul; Maji, Bibekananda and Zaharescu, Alexandru, “Zeros of combinations of the Riemann Ξ-function and the confluent hypergeometric function on bounded vertical shifts”, Journal of Mathematical Analysis and Applications, DOI: 10.1016/j.jmaa.2018.05.072, Jun. 2018. en_US
dc.identifier.issn 0022-247X
dc.identifier.uri https://repository.iitgn.ac.in/handle/123456789/3749
dc.identifier.uri https://doi.org/10.1016/j.jmaa.2018.05.072
dc.description.abstract In 1914, Hardy proved that infinitely many non-trivial zeros of the Riemann zeta function lie on the critical line using the transformation formula of the Jacobi theta function. Recently the first author obtained an integral representation involving the Riemann Ξ-function and the confluent hypergeometric function linked to the general theta transformation. Using this result, we show that a series consisting of bounded vertical shifts of a product of the Riemann Ξ-function and the real part of a confluent hypergeometric function has infinitely many zeros on the critical line, thereby generalizing a previous result due to the first and the last authors along with Roy and Robles. The latter itself is a generalization of Hardy's theorem. en_US
dc.description.statementofresponsibility by Atul Dixit
dc.description.statementofresponsibility Atul Dixit,; Rahul Kumar, Bibekananda Maji and Alexandru Zaharescu
dc.language.iso en en_US
dc.publisher Elsevier en_US
dc.subject Riemann zeta function en_US
dc.subject Theta transformation en_US
dc.subject Confluent hypergeometric function en_US
dc.subject Bounded vertical shifts en_US
dc.subject Zeros en_US
dc.title Zeros of combinations of the Riemann Ξ-function and the confluent hypergeometric function on bounded vertical shifts en_US
dc.type Article en_US
dc.relation.journal Journal of Mathematical Analysis and Applications


Files in this item

Files Size Format View

There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record

Search Digital Repository


Browse

My Account