Skip to main content Accessibility help

A disproof of a conjecture of Pólya

  • C. B. Haselgrove (a1)


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.



Hide All
1.Haselgrove, C. B. and Miller, J. C. P., Tables of the Riemann zeta function (Royal Society Mathematical Tables, Vol. 6) (in the press).
2.Ingham, A. E., “On two conjectures in the theory of numbers”, American J. of Math., 64 (1942), 313319.
3.Lehmer, D. H., “Extended computation of the Riemann zeta function”, Mathemalika, 3 (1956), 102108.
4.Mertens, F., “Uber eine zahlentheoretische Funktion”, Sitzungsberichte Akad. Wien., 106, Abt. 2a (1897), 761830.
5.Pólya, G., “Verschiedene Bemerkungen zur Zahlentheorie”, Jahresbericht der deutschen Math. Vereinigung, 28 (1919), 3140.
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).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed