JournalsrsmupVol. 127falsepp. 179–192

Riccati Differential Equation for Hypergeometric Differential Equation

  • Takahiro Nakagawa

    Chiba University, Japan
Riccati Differential Equation for Hypergeometric Differential Equation cover

Abstract

In this paper, we study the solutions of Riccati differential equation corresponding to pp-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 Q(t)\mathbb{Q}(t) have, for almost all prime, a solution in rational function field over the finite field Fp\mathbb{F}_p, 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. 179–192

DOI 10.4171/RSMUP/127-9