Unformatted text preview: prime p (cf.(220.127.116.11)). As C varies over the integers l<C<n-1, the characters Z(-C) run over a Q-conjugacy class of irreducible repre- sentations of#, (namely, the faithful ones). Thus we may apply Theorem 5.7 to deduce that for every integer C >__ 1 invertible modulo n, (18.104.22.168) P(X(-C)) H~,(X (n; A, B, C)) with the Gauss-Manin connection has a full set of algebraic solutions. By (22.214.171.124), it follows that for every integer C> 1 which is invertible modulo n, in particular for C = 1, the hypergeometric module (126.96.36.199) E (C a/n, C b/n, C c/n)[ C (2) has a full set of algebraic solutions. Q.E.D. (6.9.4) Corollary. Let a, b, c, n be integers, n >_ 1, and suppose none of the exponent d!fference (188.8.131.52) 1 - c/n, c/n - a/n - b/n, a/n - b/n is an integer. Then the hypergeometric equation with parameters a/n, b/n, c/n has two algebraic solutions ![ and only if, for every integer 1 <- C <- n- 1...
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This note was uploaded on 12/21/2011 for the course MAP 4341 taught by Professor Normankatz during the Fall '11 term at UNF.
- Fall '11