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Let be a number field, and suppose is irreducible over . Using algebraic geometry and group theory, we describe conditions under which the -exceptional set of , i.e. the set of for which the specialized polynomial is -reducible, is finite. We give three applications of the methods we develop. First, we show that for any fixed , all but finitely many -specializations of the degree generalized Laguerre polynomial are -irreducible and have Galois group . Second, we study specializations...
In this work we compute the Stokes matrices of the ordinary differential equation satisfied by the hypergeometric integrals associated to an arrangement of hyperplanes in generic position. This generalizes the computation done by J.-P. Ramis for confluent hypergeometric functions, which correspond to the arrangement of two points on the line. The proof is based on an explicit description of a base of canonical solutions as integrals on the cones of the arrangement, and combinatorial relations between...
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