In this paper, we study the solutions of Riccati differential equation correspondingto -adic differential equations which are solvable on the generic disc. As an application, we consider the Grothendieck conjecture for Riccati differential equations. We see that the Riccati differential equations for some globally nilpotent differential equation with coefficients in have, for almost all prime, a solution in rational function field over the finite field , but do not have any algebraic solutions.
Cite this article
Takahiro Nakagawa, Riccati Differential Equation for Hypergeometric Differential Equation. Rend. Sem. Mat. Univ. Padova 127 (2012), pp. 179–192DOI 10.4171/RSMUP/127-9