Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-23T10:04:58.909Z Has data issue: false hasContentIssue false
  • English
  • Français

A disproof of a conjecture of Pólya

Published online by Cambridge University Press:  26 February 2010

C. B. Haselgrove
C. B. Haselgrove
Affiliation:
The University, Manchester 13.
Get access

Extract

Let λ(n) be Liouville's function denned by

where v is the number of prime factors of n, repeated factors being counted according to their multiplicity. Alternatively, λ(n) may be denned by the relation

where ζ(s) is the zeta function of Riemann.

Type
Research Article
Information
Mathematika , Volume 5 , Issue 2 , December 1958 , pp. 141 - 145
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

1.Haselgrove, C. B. and Miller, J. C. P., Tables of the Riemann zeta function (Royal Society Mathematical Tables, Vol. 6) (in the press).Google Scholar
2.Ingham, A. E., “On two conjectures in the theory of numbers”, American J. of Math., 64 (1942), 313–319.CrossRefGoogle Scholar
3.Lehmer, D. H., “Extended computation of the Riemann zeta function”, Mathemalika, 3 (1956), 102–108.CrossRefGoogle Scholar
4.Mertens, F., “Uber eine zahlentheoretische Funktion”, Sitzungsberichte Akad. Wien., 106, Abt. 2a (1897), 761–830.Google Scholar
5.Pólya, G., “Verschiedene Bemerkungen zur Zahlentheorie”, Jahresbericht der deutschen Math. Vereinigung, 28 (1919), 31–40.Google Scholar
6.Turán, P., “On some approximative Dirichlet-polynomials in the theory of the zetafunction of Riemann”, Danske Vid. Selsk. Mat.-Fys. Medd., 24, No. 17 (1948).Google Scholar