On instances of Fox’s integral equation connection to the Riemann zeta function
Archivum Mathematicum (2019)
- Volume: 055, Issue: 3, page 195-201
- ISSN: 0044-8753
Access Full Article
top
Abstract
topHow to cite
topPatkowski, Alexander E.. "On instances of Fox’s integral equation connection to the Riemann zeta function." Archivum Mathematicum 055.3 (2019): 195-201. <http://eudml.org/doc/294381>.
@article{Patkowski2019,
abstract = {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.},
author = {Patkowski, Alexander E.},
journal = {Archivum Mathematicum},
keywords = {Fourier integrals; Fox’s integral equation; Riemann prime counting function},
language = {eng},
number = {3},
pages = {195-201},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On instances of Fox’s integral equation connection to the Riemann zeta function},
url = {http://eudml.org/doc/294381},
volume = {055},
year = {2019},
}
TY - JOUR
AU - Patkowski, Alexander E.
TI - On instances of Fox’s integral equation connection to the Riemann zeta function
JO - Archivum Mathematicum
PY - 2019
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 055
IS - 3
SP - 195
EP - 201
AB - 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.
LA - eng
KW - Fourier integrals; Fox’s integral equation; Riemann prime counting function
UR - http://eudml.org/doc/294381
ER -
References
top- Erdélyi, A. (ed.), Tables of Integral Transforms, vol. 1, McGraw-Hill, New York, 1954. (1954)
- Fox, C., Applications of Mellin’s transformations to integral equations, Proc. Roy. Soc. London 39 (1933), 495–502. (1933) MR1576330
- Ivic, A., Some identities of the Riemann zeta function II, Facta Univ. Ser. Math. Inform. 20 (2005), 1–8. (2005) MR2185962
- Paris, R.B., Kaminski, D., Asymptotics and Mellin–Barnes Integrals, Cambridge University Press, 2001. (2001) MR1854469
- Titchmarsh, E.C., Introduction to the Theory of Fourier Integrals, 2nd ed., Oxford University Press, Oxford, 1959. (1959) MR3155290
- Titchmarsh, E.C., The theory of the Riemann zeta function, 2nd ed., Oxford University Press, 1986. (1986) MR0882550
- Zemyan, S.M., The Classical Theory of Integral equations: A Concise Treatment, Birkhäuser, Boston, 2012. (2012) MR2952229
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.