Unformatted text preview: finite ~tale covering of S c. (6.2.2) There exists a finite extension of the field C(2) over which E(a, b,c) becomes trivial. (6.2.3) The hypergeometric equation (6.1.2) with parameters a, b, c has a full set of algebraic solutions (cf. (5.4.2.1)). (6.2.4) The hypergeometric equation (6.1.2) with parameters a, b, c, has a finite monodromy group. (6.2.5) The inverse image of E (a, b, c) on C0.)/C has pcurvature zero for almost all primes p (cf. (5.4.3.2)). (6.2.6) The parameters a, b, c are all rational numbers, and for almost all primes p, the reduction modulo p of the hypergeometric equation (6.1.2) with parameters a, b, c has two solutions in Fp [2] (resp. Fp (2), resp. Fp[[2]], resp. Fp((2))) which are linearly independent over Fp(2 p) (resp. F(2P), resp. Fp(2"), resp. Fp((2P)))....
View
Full Document
 Fall '11
 NormanKatz
 Empty set, Rational number, Algebraic Solutions of Differential Equations, hypergeometric equation

Click to edit the document details