ALGEBRAIC DEGREE OF SERIES OF RECIPROCAL ALGEBRAIC INTEGERS

We give sufficient conditions for any linear combination over Q of numbers S-n=1(8) b(1,n)/a(1,n), . . ., S-n=1(8) b(K,n)/a(K,n )to have algebraic degree greater than an arbitrary fixed integer D when the numbers ai,n are algebraic integers of sufficiently rapidly increasing modulus and the b(i,n) are positive integers that are not too large.