.121221222\dots is not quadratic (Q2574709)
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: .121221222\dots is not quadratic |
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | .121221222\dots is not quadratic |
scientific article |
Statements
.121221222\dots is not quadratic (English)
0 references
30 November 2005
0 references
The main result of this paper is the following theorem. Theorem: Let \(b>1\) be an integer, \(f(X)\) be an integer valued quadratic polynomial with positive leading term. Assume that \(\{a_n\}_{n=0}^\infty\) is a bounded sequence of positive integers. Then the number \(\sum_{n=0}^\infty \frac{a_n}{b^{f(n)}}\) is not algebraic of degree \(\leq 2\). The proof is based on the gap theory.
0 references
irrationality
0 references
infinite series
0 references
\(p\)-adic numbers
0 references
