1,720,967 research outputs found
On twisted A-harmonic sums and Carlitz finite zeta values
Full text linkTwisted A-harmonic sums are partial sums of a class of zeta values introduced by the first author. We prove some new identities for such sums and we deduce properties of analogues of finite zeta values in the framework of the Carlitz module. In the theory of finite multiple zeta values as introduced by Kaneko and Zagier, finite zeta values are all zero and there is no known non-zero finite multiple zeta value. In the Carlitzian setting the phenomenology is different as we can deduce, from our results, the irrationality of certain finite zeta values
Hyperdifferential properties of drinfeld quasi-modular forms
No full textThis article is divided into two parts. In the first part we endow a certain ring of "Drinfeld quasi-modular forms" for GL 2(F9[T]) (where q is a power of a prime) with a system of "divided derivatives" (or hyperderivations). This ring contains Drinfeld modular forms as defined by Gekeler in [7], and the hyperdifferential ring obtained should be considered as a close analogue in positive characteristic of Ramanujan's famous differential system relating to the first derivatives of the classical Eisenstein series of weights 2,4, and 6. In the second part of this article, we prove that, when q /=2,3, if 9 is a nonzero hyperdifferential prime ideal, then it contains the Poincaré series h = Pq+11 of [7]. This last result is the analogue of a crucial property proved by Nesterenko [12] in characteristic zero in order to establish a multiplicity estimate. © The Author 2008. Published by Oxford University Press. All rights reserved
Sur la distance d'un point algébrique à l'origine dans les variétés abéliennes
Full text linkRésuméNous étudions les propriétés métriques des points rationnels de petite hauteur dans les variétés abéliennes. Plus précisément, tenant compte de la conjecture de Lehmer abélienne telle qu'elle a été établie par S. David et M. Hindry dans (1998, prépublications Univ. P. et M. Curie) nous avons étendu certains résultats de M. Mignotte et M. Waldschmidt (1994, J. Number Theory47, 43–62) aux variétés abéliennes définies sur un corps de nombres. Nous donnons une interprétation partiellement quantitative au principe suivant: “un point rationnel de petite hauteur de Néron–Tate non nulle ne peut pas être très près de l'origine de la variété abélienne.” Copyright 2001 Academic Press. We study the metric properties of rational points of small height over abelian varieties. More precisely, referring to the abelian Lehmer conjecture (as stated by S. David and M. Hindry in (1998, Prépublications Univ. P. et M. Curie)), we have extended some results of M. Mignotte and M. Waldschmidt in (1994, J. Number Theory47, 43–62) to abelian varieties defined over a number field. We give a partially quantitative interpretation of the following principle: “a rational point of small and non vanishing Néron–Tate height cannot be too close to the origin of the abelian variety.
Aspects de L'Indépendance algébrique en caracté ristique non nulle [d'après Anderson, Brownawell, Denis, Papanikolas, Thakur, Yu,...]
Full text linkTesto accompagnante un seminario Bourbaki su risultati recenti di indipendenza algebrica in caratteristica positiv
On certain families of Drinfeld quasi-modular forms
Full text linkThis paper deals with two problems arising in the study of Drinfeld quasi-modular forms. The first problem is to find the maximal order of vanishing at infinity of a non-zero Drinfeld quasimodular form and leads to the notion of "extremal" quasi-modular form (highest possible order of vanishing for fixed weight and depth). The second problem is determining differential properties of extremal forms, leading to the notion of "differentially extremal" form. From our investigations, we will obtain an upper bound for the order of vanishing at infinity of non-zero Drinfeld quasimodular forms of small depths. The paper ends with a collection of tools used in the previous parts. The notion of "extremal" form is similar to one introduced by Kaneko and Koike in [M. Kaneko, M. Koike, On extremal quasimodular forms, Kyushu J. Math. 60 (2006) 457-470]. © 2009 Elsevier Inc. All rights reserved
On extremal quasi-modular forms after kaneko and koike
Full text linkKaneko and Koike introduced the notion of extremal quasi-modular forms and proposed conjectures on their arithmetic properties. The aim of this paper is to prove a rather sharp multiplicity estimate for these quasi-modular forms. The paper ends with discussions and partial answers around these conjectures and an appendix by G. Nebe containing the proof of the integrality of the Fourier coefficients of the normalized extremal quasi-modular form of weight 14 and depth one
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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