Some generalizations for a theorem by Landau (Q2745650)
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scientific article; zbMATH DE number 1654981
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some generalizations for a theorem by Landau |
scientific article; zbMATH DE number 1654981 |
Statements
4 February 2002
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distribution of primes
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inequalities
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Some generalizations for a theorem by Landau (English)
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Let \(\pi(x)\) denote the number of primes not exceeding \(x\). The author proves certain interesting new inequalities involving this function. For example, for \(x\geq y\geq 2\) one has NEWLINE\[NEWLINE\pi(x+y)\leq \pi(x) + \pi(y)+\pi(x-y);NEWLINE\]NEWLINE for all \(x,y\geq 2\) the following inequality holds true: NEWLINE\[NEWLINE\pi^2(x+y)\leq 2(\pi^2(x)+\pi^2(y)).NEWLINE\]
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