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Register a new userSommes de Dedekind associees `a un corps de nombres totalement reel
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Authors
Pierre Charollois
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We define Dedekind sums attached to a totally real number field of class number one. We prove that they satisfy some reciprocity law. Then we relate them to special values of Hecke $L$-functions. We conclude that they are ruled by Starks conjecture.
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On the rank of Jacobians over function fields.} Let $f:mathcal{X}to C$ be a projective surface fibered over a curve and defined over a number field $k$. We give an interpretation of the rank of the Mordell-Weil group over $k(C)$ of the jacobian of the generic fibre (modulo the constant part) in terms of average of the traces of Frobenius on the fibers of $f$. The results also give a reinterpretation of the Tate conjecture for the surface $mathcal{X}$ and generalizes results of Nagao, Rosen-Silverman and Wazir.
We reinterpret a conjecture of Breuil on the locally analytic $mathrm{Ext}^1$ in a functorial way using $(varphi,Gamma)$-modules (possibly with $t$-torsion) over the Robba ring, making it more accurate. Then we prove several special or partial cases of this improved conjecture, notably for ${rm GL}_3(mathbb{Q}_p)$.
This document is intended to present in detail the processing criteria and the analysis techniques used for the production of the Vulnerability Map Sanitary based on the use of public and open data sources. The paper makes use of statistical analysis techniques (MCA, PCA, etc.) and machine learning (autoencoders) for the processing and analysis of information. The final product is a map at the census track level that seeks to quantify the populations access to basic health benefits.
The main objective of this dissertation is to present an adaptation of some finite volume methods used in the resolution of problems arising in sedimentation processes of flocculated suspensions (or sedimentation with compression). This adaptation is based on the utilization of multiresolution techniques, originally designed to reduce the computational cost incurred in solving using high resolution schemes in the numerical solution of hyperbolic systems of conservation laws.
Consider the ring of holomorphic function germs in $C^n$ and denote by $M$ the maximal ideal of this ring. For any a holomorphic function germ $f$ with an isolated critical point, the finite determinacy theorem (Mather-Tougeron) asserts that there exists some $k$, such that $f+g$ can be brought back to $f$, via a holomorphic change of variables, for any $g in M^k$. In this paper, a generalisation of this theorem for functions defined in a neighbourhood of a Stein compact subset and for an arbitrary ideal is given.
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