- Title
- Approximations to q-logarithms and q-dilogarithms, with applications to q-zeta values
- Creator
- Zudilin, W.
- Relation
- Journal of Mathematical Sciences Vol. 137, Issue 2, p. 4673-4683
- Publisher Link
- http://dx.doi.org/10.1007/s10958-006-0263-y
- Publisher
- Springer
- Resource Type
- journal article
- Date
- 2006
- Description
- We construct simultaneous rational approximations to q-series L₁(x₁; q) and L1(x₂; q) and, if x = x₁ = x₂, to series L₁(x; q) and L₂(x; q), where [formula could not be replicated], [formula could not be replicated]. Applying the construction, we obtain quantitative linear independence over ℚ of the numbers in the following collections: 1, ζq(1) = L₁(1; q), ζq+00B2(1) and 1, ζq(1), ζq(2) = L₂(1; q) for q = 1/p, p ε ℤ {0,±1}.
- Subject
- quantitative linear independence; q-logarithms; q-series; simultaneous rational approximations
- Identifier
- http://hdl.handle.net/1959.13/934875
- Identifier
- uon:11926
- Identifier
- ISSN:1072-3374
- Rights
- The final publication is available at www.springerlink.com
- Language
- eng
- Full Text
- Reviewed
- Hits: 2645
- Visitors: 3112
- Downloads: 230
| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | SOURCE2 | Author final version | 250 KB | Adobe Acrobat PDF | View Details Download |