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The mean-value of the Riemann zeta function. (English) Zbl 0036.18603


MSC:

11M06 \(\zeta (s)\) and \(L(s, \chi)\)
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[1] G. H. Hardy andJ. E. Littlewood, Acta math. 41 (1918), 119–196. · doi:10.1007/BF02422942
[2] J. E. Littlewood, Proc. London Math. Soc. (2), 20 (1922), Records, XXII–XXVIII.
[3] A. E. Ingham, Proc. London Math. Soc. (2), 27 (1926), 273–300.
[4] E. C. Titchmarsh, Quart. J. of Math. (Oxford), 5 (1934), 195–210. · Zbl 0010.01002 · doi:10.1093/qmath/os-5.1.195
[5] The connection is to some extent apparent in my paper, Quart. J. of Math. (Oxford), 10 (1939), 122–128. I hope to go in this question more deeply in a subsequent paper.
[6] See, for instance,A. Oppenheim, Proc. London. Math. Soc. (2), 26 (1927), 295–350, and references there given. · doi:10.1112/plms/s2-26.1.295
[7] See for instanceOppenheim, loc cit. · doi:10.1112/plms/s2-26.1.295
[8] See for instance ’Modern Analysis’, (E. T. Whittaker andG. N. Watson, 4th edition Cambridge, 1927), § 5. 4.
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