Written for advanced undergraduate and first-year graduate students, this book aims to introduce students to a serious level of p-adic analysis with important implications for number theory. The main object is the study of G-series, that is, power series y=aij=0 Ajxj with coefficients in an algebraic number field K. These series satisfy a linear differential equation Ly=0 with LIK(x) d/dx] and have non-zero radii of convergence for each imbedding of K into the complex numbers. They have the further property that the common denominators of the first s...
Written for advanced undergraduate and first-year graduate students, this book aims to introduce students to a serious level of p-adic analy...
Dedicated to Philippe Robba, this conference was characterized by the discussion of numerous algebraic geometries. Other papers were devoted to exponential sums, a theme connecting p-adic analysis to number theory.
Dedicated to Philippe Robba, this conference was characterized by the discussion of numerous algebraic geometries. Other papers were devoted to expone...
The present work treats p-adic properties of solutions of the hypergeometric differential equation d2 d ( x(l - x) dx + (c(l - x) + (c - 1 - a - b)x) dx - ab)y = 0, 2 with a, b, c in 4) n Zp, by constructing the associated Frobenius structure. For this construction we draw upon the methods of Alan Adolphson 1] in his 1976 work on Hecke polynomials. We are also indebted to him for the account (appearing as an appendix) of the relation between this differential equation and certain L-functions. We are indebted to G. Washnitzer for the method used in the construction of our dual theory (Chapter...
The present work treats p-adic properties of solutions of the hypergeometric differential equation d2 d ( x(l - x) dx + (c(l - x) + (c - 1 - a - b)x) ...
