Dr. Katz DEq Homework Solutions 87

Dr. Katz DEq Homework Solutions 87 - Algebraic Solutions of...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Algebraic Solutions of Differential Equations 87 6.4. Solutions of the Hypergeometric Equation in Characteristic p (6.4.0) Proposition (compare [23]). Let a, b, c be integers contained in {0, 1, . .., p- 1}. In order that the hypergeometric equation with parameters -a,-b,-c admit two "mod p" solutions in Fp[2] which are linearly independent over Fp(2), it is necessary and sufficient that either b> c > a or a>c>b. Proof Let d--f(-a, -b, -c) denote the hypergeometric differential operator with parameters - a, - b, - c; r=((-a,-b,-c)=2(1-,~) (6.4.0.1) + [-c-(1-a-b) 2] J-~-ab. is an Fp [2P]-linear endomorphism of Fp [2], which maps the Fp-module N of polynomials of degree at most p- 1 to itself (in an Fp-linear manner).
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.
Ask a homework question - tutors are online