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Fourier integrals; Fox’s integral equation; Riemann prime counting function
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.
[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
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