Riccati Differential Equation for Hypergeometric Differential Equation
Copyright policy )Riccati Differential Equation for Hypergeometric Differential Equation
In this paper, we study the solutions of Riccati differential equation corresponding to p -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 \mathbb{Q}(t) have, for almost all prime, a solution in rational function field over the finite field \mathbb{F}_p , but do not have any algebraic solutions.
- Chiba University Japan
\(p\)-adic differential equations, Abstract differential equations, Riccati differential equations, hypergeometric differential equations, Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.), Grothendieck conjecture, algebraic solution to differential equations
\(p\)-adic differential equations, Abstract differential equations, Riccati differential equations, hypergeometric differential equations, Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.), Grothendieck conjecture, algebraic solution to differential equations
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