The mean-value of the Riemann zeta function

G. H. Hardy andJ. E. Littlewood, Acta math. 41 (1918), 119–196.

J. E. Littlewood, Proc. London Math. Soc. (2), 20 (1922), Records, XXII–XXVIII.

A. E. Ingham, Proc. London Math. Soc. (2), 27 (1926), 273–300.

E. C. Titchmarsh, Quart. J. of Math. (Oxford), 5 (1934), 195–210.

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.

See, for instance,A. Oppenheim, Proc. London. Math. Soc. (2), 26 (1927), 295–350, and references there given.

See for instanceOppenheim, loc cit.

See for instance ‘Modern Analysis’, (E. T. Whittaker andG. N. Watson, 4th edition Cambridge, 1927), § 5. 4.