Article
Full entry |
PDF
(0.4 MB)
Feedback
PDF
(0.4 MB)
Feedback
Keywords:
Fourier integrals; Fox’s integral equation; Riemann prime counting function
Fourier integrals; Fox’s integral equation; Riemann prime counting function
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.
References:
[1] Erdélyi, A. (ed.): Tables of Integral Transforms. vol. 1, McGraw-Hill, New York, 1954.
[2] Fox, C.: Applications of Mellin’s transformations to integral equations. Proc. Roy. Soc. London 39 (1933), 495–502. MR 1576330
[3] Ivic, A.: Some identities of the Riemann zeta function II. Facta Univ. Ser. Math. Inform. 20 (2005), 1–8. MR 2185962
[4] Paris, R.B., Kaminski, D.: Asymptotics and Mellin–Barnes Integrals. Cambridge University Press, 2001. MR 1854469
[5] Titchmarsh, E.C.: Introduction to the Theory of Fourier Integrals. 2nd ed., Oxford University Press, Oxford, 1959. MR 3155290
[6] Titchmarsh, E.C.: The theory of the Riemann zeta function. 2nd ed., Oxford University Press, 1986. MR 0882550
[7] Zemyan, S.M.: The Classical Theory of Integral equations: A Concise Treatment. Birkhäuser, Boston, 2012. MR 2952229
Search
Partner of
