1,720,983 research outputs found
Nonvanishing of <i>L</i>-functions, the Ramanujan Conjecture, and Families of Hecke Characters
No full textAbstractWe prove a nonvanishing result for families of GLn× GLn Rankin–Selberg L-functions in the critical strip, as one factor runs over twists by Hecke characters. As an application, we simplify the proof, due to Luo, Rudnick, and Sarnak, of the best known bounds towards the Generalized Ramanujan Conjecture at the infinite places for cusp forms on GLn. A key ingredient is the regularization of the units in residue classes by the use of an Arakelov ray class group.</jats:p
On the Ramanujan conjecture over number fields
No full textWe extend to an arbitrary number field the best known bounds towards Ramanujan for the group GLn, n=2,3,4. In particular, we present a technique which overcomes the analytic obstacles posed by the presence of an infinite group of units
Large values of Maass forms on compact quotients of hyperbolic Grassmannians in the volume aspect
No full textSoient n > m = 1 des entiers tels que n + m >= 4 soit pair. On prouve l’existence, dans l’aspect volume, de formes de Maass exceptionnelles sur des quotients compacts de la grassmanienne hyperbolique de signature (n,m). La méthode repose sur le travail de Rudnick et Sarnak, étendu par Donnelly puis généralisé par Brumley et Marshall en rang supérieur. Celle-ci combine un argument de comptage et une relation de périodes permettant de montrer qu’une certaine période distingue les relèvements thêta depuis un groupe auxiliaire. La structure de niveau est définie relativement à cette période et le groupe auxiliaire qui intervient est U(m,m) ou Sp_2m(R), de sorte que (U(n,m),U(m,m)) ou (O(n,m),Sp_2m(R)) soit une paire duale réductive de type 1. La borne inférieure s’exprime naturellement, à un facteur logarithmique près, comme le quotient des volumes avec la structure de congruence principale sur le groupe auxiliaire.Let n > m = 1 be integers such that n + m >= 4 is even. We prove the existence, in the volume aspect, of exceptional Maass forms on compact quotients of the hyperbolic Grassmannian of signature (n,m). The method builds upon the work of Rudnick and Sarnak, extended by Donnelly and then generalized by Brumley and Marshall to higher rank. It combines a counting argument with a period relation, showingthat a certain period distinguishes theta lifts from an auxiliary group. The congruence structure is defined with respect to this period and the auxiliary group is either U(m,m) or Sp_2m(R), making (U(n,m),U(m,m)) or (O(n,m),Sp_2m(R)) a type 1 dual reductive pair. The lower bound is naturally expressed, up to a logarithmic factor, as the ratio of the volumes, with the principal congruence structure on the auxiliary group
La croissance maximale des périodes automorphes et intégrales oscillatoires pour les variétés plates maximales
No full textCette thèse contribue à la théorie analytique des formes automorphes et des fonctions L automorphes. Dans une première partie nous démontrons un résultat sur les valeurs extrêmes des périodes géodésiques des formes de Hecke-Maass sur les surfaces hyperboliques compactes, quand la valeur propre du Laplacien grandit. La preuve utilise la méthode d'amplification d'Iwaniec et Sarnak. Nous obtenons aussi un résultat sur les valeurs extrêmes des fonctions L de Rankin-Selberg et nous faisons le lien avec les conjectures sur les valeurs extrêmes des fonctions L. Dans une deuxième partie nous démontrons un résultat sur les valeurs extrêmes des périodes plates maximales des formes de Hecke-Maass, sur les espaces symétriques compacts associés aux formes de PGL(3). Nous discutons de son importance dans le contexte plus large du comportement extrémal des périodes automorphes. Nous obtenons aussi une asymptotique pour des moyennes quadratiques des périodes plates maximales sur des espaces symétriques compacts plus généraux. Nos principales contributions techniques sont les suivantes. La première est l'analyse des intégrales orbitales utilisée pour obtenir des asymptotiques pour une formule de traces relative, ainsi que des nouveaux résultats sur la géométrie globale des sous-variétés plates maximales des espaces symétriques. La deuxième est une exploration des limites de la méthode d'amplification pour les périodes toriques sur les formes de PGL(n).This dissertation contributes to the analytic theory of automorphic periods and automorphic L-functions.In the first part we prove an extreme value result for geodesic periods of Hecke-Maass forms on compact arithmetic hyperbolic surfaces, as the Laplacian eigenvalue grows. The proof uses the celebrated amplification method of Iwaniec and Sarnak. We also obtain a theorem on extreme values of Rankin-Selberg L-functions and draw the connection to conjectures on the maximal size of L-functions.In the second part we prove a spectral aspect extreme value result for maximal flat periods of Hecke-Maass forms, on compact locally symmetric spaces associated to forms of PGL(3). We discuss its significance in the wider context of extreme behavior of automorphic periods. We also prove a mean square asymptotic for maximal flat periods on more general compact locally symmetric spaces.Our main technical contributions are the following. The first is the analysis of orbital integrals needed to prove asymptotics for a relative trace formula, together with new results on the global geometry of maximal flat submanifolds of symmetric spaces. The second is an exploration of the limits of the amplification method for toric periods on forms of PGL(n)
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
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Stabilized Values of the Generalized Goss Zeta Function
No full textAbstractAfter a brief review in the first section of the definitions and basic properties of the Riemann and Goss zeta functions, we begin in Section 2 the analysis of the generalized Goss zeta function by examining its stabilization properties. An idea in this section gives rise to the new concept of a stabilized ζ-polynomial, which is the main result of this paper. In Section 3, we give the general form of such polynomials for a certain equivalence class in the domain space
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