On an asymptotic formula in theory of numbers. (Q2614373)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On an asymptotic formula in theory of numbers. |
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On an asymptotic formula in theory of numbers. (English)
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1933
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Es sei \(\pi_2(x)\) die Anzahl derjenigen natürlichen Zahlen bis \(x\), die Produkte zweier verschiedenen Primzahlen sind. Mittels des Primzahlsatzes wird \[ \pi_2(x) = \dfrac{x\log\log x}{\log x} + \dfrac{Bx}{\log x} + o\bigg(\dfrac{x}{\log x}\bigg) \] bewiesen. Die Konstante \(B\) hat dabei den Wert \[ \lim\limits_{x=\infty} \bigg(\sum_{p\leqq x} \dfrac1p - \log\log x\bigg). \]
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