1. Berlin Journal für Mathematik, Vol.147, 1917, p.205–232. In the following text, P.I refers to Part I of this article.
2. Archiv d. Math. u. Phys., Vol.21, 1913, p.250. Cf. also E. Landau, Darstelling und Begruendung einiger neuerer Ergebnisse der Functionentheorie, Berlin, 1916, p.20.
3. For the case R(f(x)) > 0 a similar remark can be found (due to O. Toeplitz) in E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, p.891. Cf. also F. Riesz, Berlin Journal fuer Mathematik, Vol.146, 1915, p.85.
4. If the real part of ∑b ν x ν is positive for |x| < 1 then we clearly have |b ν | ≤ 2b0′ for ν ≥ 1. This result follows immediately from the inequality (35) if we set f(x) = x ν .
5. Muench. Ber., No.3, 1910. E. Landau gives a somewhat simpler example in Section 3 of his book cited in Footnote 2.