ТАУБЕРОВЫ ТЕОРЕМЫ С МЕДЛЕННО МЕНЯЮЩИМИСЯ С ОСТАТКОМ ФУНКЦИЯМИ И ИХ ПРИЛОЖЕНИЯ
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ID: 193092
2012
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Abstract
E. Wirsing setted up a problem in 1967 year: Is it possible to reduce the estimation ∑n≤xf(n)=o(xlogx∑n≤xf(n)n),x→∞\eqno(1) from the estimation ∑p≤xf(p)logpp=o(logx),x→∞.\eqno(2) Here n is a positive enteger, p is a prime number. Let us denote the right-side sum in formula (2) by m(x). B. V. Levin and A. S. Finelabe had proved that the statement (2) did not emply the statement (1). The function f(n) of their conterexample is such that m(x) is bounded. But if m(x) is not bounded that Wirsing problem is opened. Two the Tauberian theorems is proved in this paper and it is istablished that if m(x) is not bounded that the condition (2) is equivalent that m(e t) is slowly variating with the residual.
| Reference Key |
.2012problemy
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|---|---|
| Authors | ;ШИРОКОВ Б. М. |
| Journal | terrestrial, atmospheric and oceanic sciences |
| Year | 2012 |
| DOI |
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