enlist
发表于 2025-3-23 12:22:48
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., etc. ...
绅士
发表于 2025-3-23 16:36:36
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
发表于 2025-3-23 19:25:36
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洞察力
发表于 2025-3-23 22:19:27
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 , or to the more advanced booklet . Everything becomes simpler if one restricts oneself, as we shall do, to the case of disks.
preservative
发表于 2025-3-24 05:15:26
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., etc. ...
残废的火焰
发表于 2025-3-24 08:39:10
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镇压
发表于 2025-3-24 12:12:03
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
发表于 2025-3-24 15:16:37
Between the sound and the simple-mindedlist). In this chapter we present a definition of G-functions (inspired by Bombieri “local-to-global” setting ), 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
发表于 2025-3-24 22:07:07
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GRACE
发表于 2025-3-25 02:03:58
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 (and correct a slight mistake in loc. cit. 8.3), in