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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.
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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

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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