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This thesis is devoted to the study of certain cases of a conjecture of Greenberg and Benois on derivative of p-adic L-functions using the method of Greenberg and Stevens. We first prove this conjecture in the case of the symmetric square of a parallel weight 2 Hilbert modular form over a totally real field where p is inert and whose associated automorphic representation is Steinberg in p, assuming certain hypotheses on the conductor. This is a direct generalization of (unpublished) results of Greenberg and Tilouine. Subsequently, we deal with the symmetric square of a finite slope, elliptic, modular form which is Steinberg at p. To construct the two-variable p-adic L-function, necessary to apply the method of Greenberg and Stevens, we have to appeal to the recently developed theory of nearly overconvergent forms of Urban. We further strengthen the above result, removing the assumption that the conductor of the form is even, using the construction of the p-adic L-function by Bocherer and Schmidt. In the final chapter we recall the definition and the calculation of the algebraic L-invariant a la Greenberg-Benois, and explain how some of the above-mentioned results could be generalized to higher genus Siegel modular forms.
511.9 --- Geometry of numbers --- Theses --- Academic collection --- 511.9 Geometry of numbers
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Betriebliche Kennzahl. --- Index numbers (Economics). --- Industrial management. --- Rechnungswesen.
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Set theory --- Théorie des ensembles --- Cardinal numbers. --- Nombres cardinaux
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Set theory --- Théorie des ensembles --- Cardinal numbers. --- Nombres cardinaux --- Théorie des ensembles
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Dairy cattle --- Livestock numbers --- Zootechny --- socioeconomic organization --- Milk yield --- Cottage industry --- milk --- Diversification --- Yoghurt --- economic environment --- Belgium
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Random variables --- Variables aléatoires. --- Law of large numbers --- Loi des grands nombres --- Probabilités. --- Probabilities --- Variables aléatoires. --- Probabilités.
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Ce mémoire est une introduction à l'étude des spectres de nombres et leurs applications. Dans le premier chapitre les concepts nécessaires pour la compréhension des chapitres suivants sont définis. Le deuxième chapitre est consacré à l'étude des spectres réels. On aborde notamment les points d'accumulations des spectres, ainsi que leur densité dans l'ensemble des nombres réels et la distance entre des éléments consécutifs de certains spectres. On présente ensuite quelques applications des spectres dans d'autres domaines des mathématiques, tels que les développements universels, la fonction de normalisation dans une base réelle et le prétraiement pour un algorithme de division en ligne. Enfin, l'apparition des spectres dans la cristallographie sera illustrée et on termine avec une discussion sur les analogies qui existent entre des résultats concernant les spectres et les convolutions infinies de Bernoulli.
discrete mathematics --- spectra --- Pisot numbers --- mathématiques discrètes --- spectre --- Nombre de Pisot --- Physique, chimie, mathématiques & sciences de la terre > Mathématiques
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Historiography --- Books --- Reviews --- -Books --- -Library materials --- Publications --- Bibliography --- Cataloging --- International Standard Book Numbers --- Historical criticism --- History --- Authorship --- Criticism --- Theses --- -Reviews --- Library materials --- Historiography - Scandinavia. --- Books - Scandinavia - Reviews - Periodicals. --- Historiographie scandinave --- Histoire --- Périodiques
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512.552.7 --- Algebraic fields --- Rings (Algebra) --- Algebraic rings --- Ring theory --- Algebraic number fields --- Algebraic numbers --- Fields, Algebraic --- Algebra, Abstract --- Algebraic number theory --- Semigroup and group rings --- 512.552.7 Semigroup and group rings --- Algèbres commutatives --- Algèbres commutatives --- Corps et polynomes
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