| Title:
|
On instances of Fox’s integral equation connection to the Riemann zeta function (English) |
| Author:
|
Patkowski, Alexander E. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
55 |
| Issue:
|
3 |
| Year:
|
2019 |
| Pages:
|
195-201 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider some applications of the singular integral equation of the second kind of Fox. Some new solutions to Fox’s integral equation are discussed in relation to number theory. (English) |
| Keyword:
|
Fourier integrals |
| Keyword:
|
Fox’s integral equation |
| Keyword:
|
Riemann prime counting function |
| MSC:
|
11L20 |
| MSC:
|
42A38 |
| idZBL:
|
Zbl 07138662 |
| idMR:
|
MR3994325 |
| DOI:
|
10.5817/AM2019-3-195 |
| . |
| Date available:
|
2019-08-05T08:48:53Z |
| Last updated:
|
2020-04-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147825 |
| . |
| Reference:
|
[1] Erdélyi, A. (ed.): Tables of Integral Transforms.vol. 1, McGraw-Hill, New York, 1954. |
| Reference:
|
[2] Fox, C.: Applications of Mellin’s transformations to integral equations.Proc. Roy. Soc. London 39 (1933), 495–502. MR 1576330 |
| Reference:
|
[3] Ivic, A.: Some identities of the Riemann zeta function II.Facta Univ. Ser. Math. Inform. 20 (2005), 1–8. MR 2185962 |
| Reference:
|
[4] Paris, R.B., Kaminski, D.: Asymptotics and Mellin–Barnes Integrals.Cambridge University Press, 2001. MR 1854469 |
| Reference:
|
[5] Titchmarsh, E.C.: Introduction to the Theory of Fourier Integrals.2nd ed., Oxford University Press, Oxford, 1959. MR 3155290 |
| Reference:
|
[6] Titchmarsh, E.C.: The theory of the Riemann zeta function.2nd ed., Oxford University Press, 1986. MR 0882550 |
| Reference:
|
[7] Zemyan, S.M.: The Classical Theory of Integral equations: A Concise Treatment.Birkhäuser, Boston, 2012. MR 2952229 |
| . |
