On instances of Fox’s integral equation connection to the Riemann zeta function

Alexander E. Patkowski

Archivum Mathematicum (2019)

  • Volume: 055, Issue: 3, page 195-201
  • ISSN: 0044-8753

Abstract

top
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.

How to cite

top

Patkowski, 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
  1. Erdélyi, A. (ed.), Tables of Integral Transforms, vol. 1, McGraw-Hill, New York, 1954. (1954) 
  2. Fox, C., Applications of Mellin’s transformations to integral equations, Proc. Roy. Soc. London 39 (1933), 495–502. (1933) MR1576330
  3. Ivic, A., Some identities of the Riemann zeta function II, Facta Univ. Ser. Math. Inform. 20 (2005), 1–8. (2005) MR2185962
  4. Paris, R.B., Kaminski, D., Asymptotics and Mellin–Barnes Integrals, Cambridge University Press, 2001. (2001) MR1854469
  5. Titchmarsh, E.C., Introduction to the Theory of Fourier Integrals, 2nd ed., Oxford University Press, Oxford, 1959. (1959) MR3155290
  6. Titchmarsh, E.C., The theory of the Riemann zeta function, 2nd ed., Oxford University Press, 1986. (1986) MR0882550
  7. Zemyan, S.M., The Classical Theory of Integral equations: A Concise Treatment, Birkhäuser, Boston, 2012. (2012) MR2952229

NotesEmbed ?

top

You must be logged in to post comments.