| dc.contributor.author |
Dixit, Atul |
|
| dc.contributor.author |
Gupta, Rajat |
|
| dc.date.accessioned |
2019-07-16T09:58:27Z |
|
| dc.date.available |
2019-07-16T09:58:27Z |
|
| dc.date.issued |
2019-06 |
|
| dc.identifier.citation |
Dixit, Atul and Gupta, Rajat, �On squares of odd zeta values and analogues of Eisenstein series�, Advances in Applied Mathematics, DOI: 10.1016/j.aam.2019.06.003, vol. 110, pp. 86-119, Sep. 2019. |
en_US |
| dc.identifier.issn |
0196-8858 |
|
| dc.identifier.uri |
https://doi.org/10.1016/j.aam.2019.06.003 |
|
| dc.identifier.uri |
https://repository.iitgn.ac.in/handle/123456789/4604 |
|
| dc.description.abstract |
A Ramanujan-type formula involving the squares of odd zeta values is obtained. The crucial part in obtaining such a result is to conceive the correct analogue of the Eisenstein series involved in Ramanujan's formula for . The formula for is then generalized in two different directions, one, by considering the generalized divisor function , and the other, by studying a more general analogue of the aforementioned Eisenstein series, consisting of one more parameter N. A number of important special cases are derived from the first generalization. For example, we obtain a series representation for , where ? is a non-trivial zero of . We also evaluate a series involving the modified Bessel function of the second kind in the form of a rational linear combination of and for . |
|
| dc.description.statementofresponsibility |
by Atul Dixit and Rajat Gupta |
|
| dc.format.extent |
vol. 110, pp. 86-119 |
|
| dc.language.iso |
en |
en_US |
| dc.publisher |
Elsevier |
en_US |
| dc.subject |
Odd zeta values |
en_US |
| dc.subject |
Modified Bessel function |
en_US |
| dc.subject |
Dedekind eta function|Ramanujan's formula |
en_US |
| dc.subject |
Irrationality |
en_US |
| dc.title |
On squares of odd zeta values and analogues of Eisenstein series |
en_US |
| dc.type |
Article |
en_US |
| dc.relation.journal |
Advances in Applied Mathematics |
|