•Journal•ISSN: 1246-7405
Journal de Theorie des Nombres de Bordeaux
Institut de Mathématiques de Bordeaux
About: Journal de Theorie des Nombres de Bordeaux is an academic journal published by Institut de Mathématiques de Bordeaux. The journal publishes majorly in the area(s): Number theory & Algebraic number field. It has an ISSN identifier of 1246-7405. It is also open access. Over the lifetime, 1142 publications have been published receiving 12759 citations. The journal is also known as: Séminaire de théorie des nombres de Bordeaux & Séminaire de théorie des nombres de Bordeaux.
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406 citations
TL;DR: In this article, the conditions générales d'utilisation (http://www.numdam.org/legal.cedram.php) of the agreement are discussed, i.e., every copie ou impression de ce fichier doit contenir la présente mention de copyright.
Abstract: © Université Bordeaux 1, 1993, tous droits réservés. L’accès aux archives de la revue « Journal de Théorie des Nombres de Bordeaux » (http://jtnb.cedram.org/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
323 citations
TL;DR: In this paper, a bibliography of recent papers on lower bounds for discriminants of number fields and related topics is presented, and the main methods, results, and open problems are discussed.
Abstract: 2014 A bibliography of recent papers on lower bounds for discriminants of number fields and related topics is presented. Some of the main methods, results, and open problems are discussed.
182 citations
TL;DR: In this article, a generalization of Bernoulli numbers referred to as poly-Bernoulli number was introduced, which is a different generalization than the generalized Bernouli numbers introduced in Chap. 4.
Abstract: In this chapter, we define and study a generalization of Bernoulli numbers referred to as poly-Bernoulli numbers, which is a different generalization than the generalized Bernoulli numbers introduced in Chap. 4.
177 citations
TL;DR: In this article, the relation between classical modular forms and Katz's overconvergent forms was clarified by using rigid analysis, and a conjecture of Gouvea was shown to be true.
Abstract: The purpose of this article is to use rigid analysis to clarify the relation between classical modular forms and Katz’s overconvergent forms. In particular, we prove a conjecture of F. Gouvea [G, Conj. 3] which asserts that every overconvergent p-adic modular form of sufficiently small slope is classical. More precisely, let p > 3 be a prime, K a complete subfield of Cp, N be a positive integer such that (N, p) = 1 and k an integer. Katz [K-pMF] has defined the spaceMk(Γ1(N)) of overconvergent p-adic modular forms of level Γ1(N) and weight k over K (see §2) and there is a natural map from weight k modular forms of level Γ1(Np) with trivial character at p to Mk(Γ1(N)). We will call these modular forms classical modular forms. In addition, there is an operator U on these forms (see [G-ApM, Chapt. II §3]) such that if F is an overconvergent modular form with q-expansion F (q) = ∑ n≥0 anq n then UF (q) = ∑
163 citations