Length of the Sum and Product of Algebraic Numbers
โ Scribed by A. Dubickas; C. J. Smyth
- Publisher
- SP MAIK Nauka/Interperiodica
- Year
- 2005
- Tongue
- English
- Weight
- 122 KB
- Volume
- 77
- Category
- Article
- ISSN
- 0001-4346
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Closed expressions are obtained for sums of products of Bernoulli numbers of the form ( 2n 2j 1 , ..., 2jN ) B 2j1 } } } B 2jN , where the summation is extended over all nonnegative integers j 1 , ..., j N with j 1 + j 2 + } } } + j N =n. Corresponding results are derived for Bernoulli polynomials,
Algebraic independence of the numbers -(%ah . .-, sequence of integers satisfying a binary linear recurrence relation and { b h ] h ~o is a periodic sequence of algebraic numbers not identically zero, are studied.
We extend a well-known formula for sums of products of two Bernoulli numbers to that of Carlitz's q-Bernoulli numbers. Recently Dilcher (J. Number Theory 60 (1996), 23 41) generalized the formula for sums of products of any number of Bernoulli numbers, but it is not easy to prove the generalized for