Some series involving Euler's function. (Q1445017)
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scientific article; zbMATH DE number 2581357
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some series involving Euler's function. |
scientific article; zbMATH DE number 2581357 |
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Some series involving Euler's function. (English)
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1927
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\(\varphi(\nu)\) sei die Eulersche, \(\mu(\nu)\) die Möbiussche zahlentheoretische Funktion. Dann werden, unter \(u\) eine feste komplexe Zahl verstanden, die Summen abgeschätzt \[ \sum \left(\frac{\nu}{\varphi(\nu)}\right)^u \frac{1}{\nu}, \quad \sum \left(\frac{\nu}{\varphi(\nu)}\right)^u \frac{|\mu(\nu)|}{\nu}, \quad \sum \left(\frac{\nu}{\varphi(\nu)}\right)^u \frac{\mu(\nu)}{\nu}. \]
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