Shorey, T. N.
(1974)
*On the sum Σ _{k=1}^{3} | 2^{πk} - α_{k} |, αk algebraic numbers*
Journal of Number Theory, 6
(4).
pp. 248-260.
ISSN 0022-314X

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Official URL: http://www.sciencedirect.com/science/article/pii/0...

Related URL: http://dx.doi.org/10.1016/0022-314X(74)90018-3

## Abstract

If α_{1}, α_{2}, α_{3} are algebraic numbers satisfying (i) the height of α_{1},α_{2}, α_{3} do not exceed H (ii) the degree of the field generated by α_{1},α_{2}, α_{3} over the field of rational numbers do not exceed D, then a positive lower bound for Σ_{k=1}^{3} | 2π^{k} - αk| is determined explicitly (except for an absolute constant) in terms of D and H.

Item Type: | Article |
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ID Code: | 67770 |

Deposited On: | 31 Oct 2011 05:58 |

Last Modified: | 31 Oct 2011 13:21 |

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