Wronskien et équations différentielles p-adiques

• Autorzy: Jean-Paul Bézivin
• Języki publikacji: FR EN

Abstrakty

EN

We prove an inequality linking the growth of a generalized Wronskian of m p-adic power series to the growth of the ordinary Wronskian of these m power series. A consequence is that if the Wronskian of m entire p-adic functions is a non-zero polynomial, then all these functions are polynomials. As an application, we prove that if a linear differential equation with coefficients in ℂₚ[x] has a complete system of solutions meromorphic in all ℂₚ, then all the solutions of the differential equation are rational functions. This is also the case when the linear differential equation has coefficients in ℚ[x], and has, for an infinity of prime numbers p, a complete system of meromorphic solutions in a disc of ℂₚ with radius strictly greater than 1.

Kategorie tematyczne

• 11S80: Other analytic theory (analogues of beta and gamma functions, p -adic integration, etc.)
• 12H25: p -adic differential equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 158
• Numer: 1
• Strony: 61-78

Daty

wydano

2013

Twórcy

autor

Jean-Paul Bézivin

• 1, Allée Edouard Quincey, 94200, Ivry-sur-Seine, France

Identyfikatory

DOI

10.4064/aa158-1-4