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1 r i .

––––\3 Xs~l SI

* + i Jv

-1 sin 2m + i)xdx,

2 F8

and so

y f < y l

-^ Jy -^ ’Jy

^^-jF’-1 ->o.
4

This proves (6), and so (5); and (2) follows from (4) and
(5) by addition.

3. The proof of (3) given here was suggested by one
given by Cramér and attributed by him to M. Riesz[1]. This
proof depends on the formulae

dx

(7)

i X 7 sin 2mnx
n j^j m

I have merely used (1) instead of (8), which simplifies the
proof considerably, as no preliminary transformation of £ (s)
is required.

Litteraturanmeldelser.

Sophus Lie, Gesammelte Abhandlungen. Auf Grund
einer Bewilligung aus dem norwegischen Forschungsfonds von
1914 und mit Unterstützung der Vidensskapsselskap zu Kristiania
und der Akademie der Wissenschaften zu Leipzig herausgegeben
von dem norwegischen matematischen Verein durch Friederich
Engel und Poul Heegaard. – Dritter Band.
Abhandlungen zur Theorie der Differentialgleichungen.

[1]
See H. Cramer, »Sur une classe de séries de Dirichlet«, Dissertation
Uppsala 1917, p. 9--10; G. H. Hardy and J. E. Littlewood, »The zeros
of Riemann’s Zeta-function on the critical line«, Mathematische
Zeitschrift, 10 (1921), p. 284--285.

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