, Volume 41, Issue 1, pp 119-196

Contributions to the theory of the riemann zeta-function and the theory of the distribution of primes

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Some of the results of which this memoir contains the first full account have already been stated shortly and incompletely in the following notes and abstracts.G. H. Hardy: (1) ‘On the zeros ofRiemann's Zeta-function’,Proc. London Math. Soc. (records of proceedings at meetings), ser. 2, vol. 13, 12, March 1914, p. xxix; (2) ‘Sur les zéros de la fonction ζ(s), deRiemann’,Comptes Rendus, 6 April 1914.J. E. Littlewood: ‘Sur la distribution des nombres premiers’,Comptes Rendus, 22 June 1914.G. H. Hardy andJ. E. Littlewood: (1) ‘New proofs of the prime-number theorem and similar theorems’,Quarterly Journal, vol. 46, 1915, pp. 215–219; (2) ‘On the zeros of theRiemann Zeta-function’ and (3) ‘On an assertion ofTschebyschef’,Proc. London Math. Soc. (records etc.), ser. 2, vol. 14, 1915, p. xiv.