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On a problem of Barban and Vehov

Published online by Cambridge University Press:  26 February 2010

Matti Jutila
Matti Jutila
Affiliation:
Department of Mathematics, University of Turku, Turku, Finland
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Extract

Barban and Vehov posed in [1] the problem of minimizing the quadratic form

under the conditions

where 1 ≤ z1 < z2 and μ(n) is the Möbius function. They also commented on the connections of this problem with zero-density estimates of L-functions near the lines δ = 1 and ½, and with Linnik's prime number theorem. This program was carried out some years later by other authors, in the first place by Selberg [10], and later by Motohashi ([7]–[9]), Graham [2] and the present author ([4], [5]).

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Type
Research Article
Information
Mathematika , Volume 26 , Issue 1 , June 1979, pp. 62 - 71
Copyright
Copyright © University College London 1979

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References

1.Barban, M. B. and Vehov, P. P.. “On an extremal problem” (in Russian), Trudy Mosk. Mat. Obsc., 18 (1968), 83–90. See also: Trans. Moscow Math. Soc, 18 (1968), 91–99.Google Scholar
2.Graham, S.. Applications of sieve methods. Dissertation (Univ. of Michigan, Ann Arbor, 1977).Google Scholar
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4.Jutila, M.. “On Linnik's constant”, Math. Scand., 41 (1977), 45–62.Google Scholar
5.Jutila, M.. “Zeros of the zeta-function near the critical line” (to appear).Google Scholar
6.Motohashi, Y.. “On a problem in the theory of sieve methods” (in Japanese), Res. Inst. Math. Sci. Kyoto Univ. Kōkyuroko, 222 (1974), 9–50.Google Scholar
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11.Titchmarsh, E. C.. The theory of the Riemann zeta-function (Clarendon Press, Oxford, 1951).Google Scholar