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On the averages of some arithmetical functions of two variables

Published online by Cambridge University Press:  26 February 2010

H. Heilbronn
H. Heilbronn
Affiliation:
Department of Mathematics, University of Bristol, Bristol 8.
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Extract

The object of this paper is to prove theorems of the following type.

THEOREM 1. If p and q are restricted to odd primes, anddenotes the Legendre symbol, then for x > 2

Type
Research Article
Information
Mathematika , Volume 5 , Issue 1 , June 1958 , pp. 1 - 7
Copyright
Copyright © University College London 1958

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References

page 2 note † Pólya, G., Göttinger Nachr. (1918), 21–29.Google Scholar I. Sehur, ibid., 30–36.

page 3 note † Nachr, Göttinger. (1917), 299–318Google Scholar, and Math. Zeitschrift, 6 (1920), 11–51.CrossRefGoogle Scholar Another reference, easier to verify, is Landau, E., Math. Zeitschrift, 2 (1918), 52–154CrossRefGoogle Scholar, Satz LXI.

page 3 note ‡ For a detailed proof see Landau, E., Acta Math., 35 (1912), 271–294CrossRefGoogle Scholar, Hilfssatz 3.

page 6 note † For a discussion of the conductors of Kummer fields see Hasse, H., Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlen, Teil II (1930), §10, XIII.Google Scholar