On the Remainder in a Series of Mertens

نویسنده

  • Peter Lindqvist
چکیده

In 1873 Mertens proved the existence of the limit B =limx!1(Pp x 1p log logx). Healso gave an expansion for the numerical evaluation of B, involving zeta values. In thispaper we estimate the error in this expansion and compute B with several hundreds ofdecimals. Our approach depends on the knowledge of the sum of a certain Lambert series.Classi cation: 11A41

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تاریخ انتشار 2007