On the sum Σk=13 | 2πk - αk |, αk algebraic numbers

Shorey, T. N. (1974) On the sum Σk=13 | 2πk - αk |, αk algebraic numbers Journal of Number Theory, 6 (4). pp. 248-260. ISSN 0022-314X

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


If α1, α2, α3 are algebraic numbers satisfying (i) the height of α12, α3 do not exceed H (ii) the degree of the field generated by α12, α3 over the field of rational numbers do not exceed D, then a positive lower bound for Σk=13 | 2πk - αk| is determined explicitly (except for an absolute constant) in terms of D and H.

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