Consequences of a theorem of Erdős-Prachar (Q2782172)
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: Consequences of a theorem of Erdős-Prachar |
scientific article; zbMATH DE number 1727716
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Consequences of a theorem of Erdős-Prachar |
scientific article; zbMATH DE number 1727716 |
Statements
28 April 2002
0 references
sequences
0 references
convergence of series
0 references
prime numbers
0 references
composite numbers
0 references
asymptotic formulae
0 references
Erdős-Prachar theorem
0 references
Consequences of a theorem of Erdős-Prachar (English)
0 references
The author studies the convergence of the series \(\sum^{\infty}_{n=1}\left|{n+1\over p_{n+1}}-{n\over p_n}\right|^\alpha\) and asymptotic behaviour of the sums \(\sum_{p_n\leq x}\left|{c_{n+1}\over p_{n+1}}-{c_n\over p_n}\right|\) and \(\sum_{p_n\leq x}\left|{p_{n+1}\over c_{n+1}}-{p_n\over c_n}\right|\), where \(p_n\) denotes the \(n\)th prime number and \(c_n\) stands for the \(n\)th composite number. The Erdős-Prachar theorem cited in the title is presented in [\textit{P. Erdős} and \textit{K. Prachar}, Abh. Math. Semin. Univ. Hamb. 25, 251-256 (1962; Zbl 0107.26601)].
0 references
