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Lower bounds for \(\sum h(m)/m\) for arithmetical functions \(h\) similar to real residue-characters. (English) Zbl 0144.27803

MSC:

11N56 Rate of growth of arithmetic functions

Keywords:

number theory
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References:

[1] Bateman, P. T., Theorems implying the non-vanishing of ∑ \(_χ(m)m^{−1}\) for real residue-characters, J. Indian Math. Soc. (N.S.), 23, 101-115 (1959/1961) · Zbl 0228.10021
[2] Bombieri, E., Limitazioni riguardanti somme di caratteri reali e somme di funzioni completamente multiplicative, Ist. Lombardo Accad. Sci. Lett. Rend., A94, 642-649 (1960) · Zbl 0103.03301
[3] Fawaz, A. Y., The explicit formula for \(L_0(x)\), (Proc. London Math. Soc., 1 (1951)), 86-103, (3) · Zbl 0042.27302
[4] Gelfond, A. O., On an elementary approach to some problems from the field of the distribution of prime numbers, Vestnik Moskov. Univ. Ser. Fiz.-Mat. Estest. Nauk, 8, 21-26 (1953), (Russian) · Zbl 0051.03401
[5] Goldsmith, D. L., On a result of E. Bombieri concerning Dirichlet’s \(L\)-functions, Ist. Lombardo Accad. Sci. Lett. Rend., A99, 662-668 (1965) · Zbl 0163.04303
[6] Haselgrove, C. B., A disproof of a conjecture of Pólya, Mathematika, 5, 141-145 (1958) · Zbl 0085.27102
[7] Ingham, A. E., On two conjectures in the theory of numbers, Amer. J. Math., 64, 313-319 (1942) · Zbl 0063.02974
[8] Landau, E., Über einen Satz von Tschebyschef, Math. Ann., 61, 527-550 (1905)
[9] Lehman, R. S., On Liouville’s function, Math. Comp., 14, 311-320 (1960) · Zbl 0103.03204
[10] Wilf, H. S., On the monotonicity of certain Riesz means, J. London Math. Soc., 37, 121-122 (1962) · Zbl 0107.26702
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