A Course in p-adic Analysis

@inproceedings{Robert2000ACI,
  title={A Course in p-adic Analysis},
  author={Alain M. Robert},
  year={2000}
}
1 p-adic Numbers.- 2 Finite Extensions of the Field of p-adic Numbers.- 3 Construction of Universal p-adic Fields.- 4 Continuous Functions on Zp.- 5 Differentiation.- 6 Analytic Functions and Elements.- 7 Special Functions, Congruences.- Specific References for the Text.- Tables.- Basic Principles of Ultrametric Analysis.- Conventions, Notation, Terminology. 

THE WORLD OF p-ADIC NUMBERS AND p-ADIC FUNCTIONS

We give a brief and elementary introduction to p-adic numbers and p-adic functions. Some of the topics are: non-archimedean valuations and the ultrametric topology, completions of Q, the Hasse

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A Note on Complex p-Adic Exponential Fields

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In this paper we apply Ax-Schanuel’s Theorem to the ultraproduct of p-adic fields in order to get some results towards algebraic independence of p-adic exponentials for almost all primes p.

Computing p-adic L-functions of totally real number fields

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On the order of vanishing of the cyclotomic p-adic L-function

For a newform for Gamma_0(N) of even weight k, we prove that its attached p-adic L-function is not identically zero on the group Z_p of the p-adic units. If p >3, we prove that the order of vanishing

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For a newform f for Γ0(N) of even weight k supersingular at a prime p ≥ 5, by using infinite dimensional p-adic analysis, we prove that the p-adic L-function Lp(f,α; χ) has finite order of vanishing

ON A q-ANALOGUE OF THE p-ADIC GENERALIZED TWISTED L-FUNCTIONS AND p-ADIC q-INTEGRALS

The purpose of this paper is to define generalized twisted q-Bernoulli numbers by using p- adic q-integrals. Furthermore, we construct a q-analogue of the p-adic generalized twisted L-functions which

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We study groups of automorphisms and birational transformations of quasi-projective varieties. Two methods are combined; the first one is based on p-adic analysis, the second makes use of
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