Titlebook: G-Functions and Geometry; A Publication of the Yves André Book 1989 Springer Fachmedien Wiesbaden 1989 Algebra.Arithmetik.Differentialgleic

enlist

https://doi.org/10.1007/978-3-658-10777-2We come nack to the general p-adic setting of IV 1,2. Thus k denotes an algebraically closed field of characteristic 0 complete under a ultrametric absolute value || with residue field of characteritic p > 0, E. stands for the complete ring of analytic elements in D(0,1), E. = E. ⊗., k[x]., etc. ...

绅士

https://doi.org/10.1007/978-3-658-07442-51.1. In this logically independent chapter, we present various generalizations of the Borel-Dwork criterion; all of them are derived from a single “main criterion” whose proof relies on the diophantine method already used in the last chapter, namely Gel’fond’s method at several places.

吸气

洞察力

Fuchsian Differential Systems: Arithmetic TheoryWe record here all the properties of p-adic analytic functions (and prove some of them) which will be used in the sequel of the book. We refer the reader to the general introduction [41], or to the more advanced booklet [26]. Everything becomes simpler if one restricts oneself, as we shall do, to the case of disks.

preservative

Local MethodsWe come nack to the general p-adic setting of IV 1,2. Thus k denotes an algebraically closed field of characteristic 0 complete under a ultrametric absolute value || with residue field of characteritic p > 0, E. stands for the complete ring of analytic elements in D(0,1), E. = E. ⊗., k[x]., etc. ...

残废的火焰

镇压

Das Elend des Kompetenzbegriffsitute a new topic: they were brought in by C.L.Siegel in 1929, in his famous paper on applications of diophantine approximation. He defined G-functions to be the formal power series y = Σa.x. whose coefficients a lie in some algebraic number field K , which fulfill the following three conditions:

declamation

Between the sound and the simple-mindedlist). In this chapter we present a definition of G-functions (inspired by Bombieri “local-to-global” setting [7]), and define two basic related invariants, namely the size Σ (which coincides with Bombieri’s one, ibid.) and the global radius. We then turn to examples: rational functions, diagonals,

慷慨不好

GRACE

https://doi.org/10.1007/978-3-658-06991-9ponding differential system (ex.3). Now we shall start from . “injective” solution (see below for the meaning of “injective”) and shall deduce information about the differential system. To this aim, we follow and simplify an idea of Chudnovsky [18] (and correct a slight mistake in loc. cit. 8.3), in