Arithmetic functions, prime counting function and polynomials (Q2911471)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Arithmetic functions, prime counting function and polynomials |
scientific article; zbMATH DE number 6074804
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Arithmetic functions, prime counting function and polynomials |
scientific article; zbMATH DE number 6074804 |
Statements
Arithmetic functions, prime counting function and polynomials (English)
0 references
31 August 2012
0 references
prime number counting function
0 references
divisor functions
0 references
Euler function
0 references
polynomials
0 references
The authors are motivated by a classical exercise stating that the prime number counting function, \(\pi(x)\), cannot be a rational function for all positive integers \(x\). The authors obtain some similar results, to the above mentioned, concerning the function \(\pi(x)\), the divisor functions \(\tau\) and \(\sigma\), and the Euler function \(\varphi\), as well as, their compositions.
0 references
