Abstract

We give sufficient conditions for any linear combination over ℚ of numbers ∑⁡n=1∞b1,n∕α1,n,…⁡,∑⁡n=1∞bK,n∕αK,n to have algebraic degree greater than an arbitrary fixed integer D when the numbers αi,n are algebraic integers of sufficiently rapidly increasing modulus and the bi,n are positive integers that are not too large.

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