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NÅGRA RELATIONER I SAMBAND MED MÖBIUS μ-FUNKTION

TORD HALL
Nordisk Matematisk Tidskrift
Vol. 20, No. 1/2 (1972), pp. 34-36
Published by: Mathematica Scandinavica
Stable URL: http://www.jstor.org/stable/24525115
Page Count: 3
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NÅGRA RELATIONER I SAMBAND MED MÖBIUS μ-FUNKTION
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Abstract

It is shown that $(1-\frac{1}{{2}^{\mathrm{s}}})\sum _{1}^{\mathrm{\infty }}\frac{(-1{)}^{\mathrm{n}-1}\mathrm{\mu }\left(\mathrm{n}\right)}{{\mathrm{n}}^{\mathrm{s}}}=(1+\frac{1}{{2}^{\mathrm{s}}})\sum _{1}^{\mathrm{\infty }}\frac{\mathrm{\mu }\left(\mathrm{n}\right)}{{\mathrm{n}}^{\mathrm{s}}}$, s = σ + it, σ ≧ 1, and a similar relation when μ(n) is replaced by |μ(n)|.

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