Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T18:56:59.100Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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