A generalization of Jarnks theorem on Diophantine approximations to Ridout type numbers Academic Article

Let s be a positive integer, c > 1 , 0 , , s c > 1,{mu _0}, ldots ,{mu _s} reals in [0, 1], = i = 0 s i sigma = Sigma _{i = 0}^s;{mu _i} , and t the number of nonzero i {mu _i} . Let i ( i = 0 , , s ) {Pi _i};(i = 0, ldots ,s) be s + 1 s + 1 disjoint sets of primes and S the set of all ( s + 1 ) (s + 1) -tuples of integers ( p 0 , , p s ) ({p_0}, ldots ,{p_s}) satisfying p 0 > 0 , p i = p i p <