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A disproof of a conjecture of Pólya

  • C. B. Haselgrove (a1)

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.

Copyright

References

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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).
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Mathematika
  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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