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Digit sums of binomial sums
- Source :
-
Journal of Number Theory . Feb2012, Vol. 132 Issue 2, p324-331. 8p. - Publication Year :
- 2012
-
Abstract
- Abstract: Let be a fixed positive integer and let be a certain type of binomial sum. In this paper, we show that for most n the sum of the digits of in base b is at least , where is some positive constant depending on b and on the sequence of binomial sums. Our results include middle binomial coefficients and Apéry numbers . The proof uses a result of McIntosh regarding the asymptotic expansions of such binomial sums as well as Bakerʼs theorem on lower bounds for nonzero linear forms in logarithms of algebraic numbers. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 0022314X
- Volume :
- 132
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 67244932
- Full Text :
- https://doi.org/10.1016/j.jnt.2011.07.004