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On instances of Fox’s integral equation connection to the Riemann zeta function. (English) Zbl 1463.42012

Author’s 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.

MSC:

42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
11L20 Sums over primes
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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 · Zbl 0011.16302
[3] Ivic, A., Some identities of the Riemann zeta function II, Facta Univ. Ser. Math. Inform. 20 (2005), 1-8 · Zbl 1199.11106
[4] Paris, R. B.; Kaminski, D., Asymptotics and Mellin-Barnes Integrals, Cambridge University Press, 2001 · Zbl 0983.41019
[5] Titchmarsh, E. C., Introduction to the Theory of Fourier Integrals, 2nd ed., Oxford University Press, Oxford, 1959 · JFM 63.0367.05
[6] Titchmarsh, E. C., The theory of the Riemann zeta function, 2nd ed., Oxford University Press, 1986 · Zbl 0601.10026
[7] Zemyan, S. M., The Classical Theory of Integral equations: A Concise Treatment, Birkhäuser, Boston, 2012 · Zbl 1270.45001
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