1,720,955 research outputs found
L-invariants for cohomological representations of PGL(2) over arbitrary number fields
Full text linkGehrmann L, Pati MR. L-invariants for cohomological representations of PGL(2) over arbitrary number fields. Forum of Mathematics, Sigma. 2024;12: e71.**Abstract**
Let
be a cuspidal, cohomological automorphic representation of an inner form
G
of
over a number field
F
of arbitrary signature. Further, let
be a prime of
F
such that
G
is split at
and the local component
of
at
is the Steinberg representation. Assuming that the representation is noncritical at
, we construct automorphic
-invariants for the representation
. If the number field
F
is totally real, we show that these automorphic
-invariants agree with the Fontaine–Mazur
-invariant of the associated
p
-adic Galois representation. This generalizes a recent result of Spieß respectively Rosso and the first named author from the case of parallel weight
to arbitrary cohomological weights.
</p
Exceptional zero formulae for anticyclotomic p-adic L-functions of elliptic curves in the ramified case
No full textIwasawa theory of modular forms over anticyclotomic Z(p)-extensions of imaginary quadratic fields K has been studied by several authors, starting from the works of Bertolini-Darmon and Iovita-Spiess, under the crucial assumption that the prime p is unramified in K. We start in this article the systematic study of anticyclotomic p-adic L-functions when p is ramified in K. In particular, when f is a weight 2 modular form attached to an elliptic curve E/Q having multiplicative reduction at p, and p is ramified in K, we show an analogue of the exceptional zeroes phenomenon investigated by Bertolini-Darmon in the setting when p is inert in K. More precisely, we consider situations in which the p-adic L-function L-p (EIK) of E over the anticyclotomic Z(p)-extension of K does not vanish identically but, by sign reasons, has a zero at certain characters x of the Hilbert class field of K. In this case we show that the value at x of the first derivative of L-p (EIK) is equal to the formal group logarithm of the specialization at p of a global point on the elliptic curve (actually, this global point is a twisted sum of Heegner points). This generalizes similar results of Bertolini-Darmon, available when p is inert in K and x is the trivial character. (C) 2018 Elsevier Inc. All rights reserved
Generalized Heegner cycles on Mumford curves
Full text linkWe study generalised Heegner cycles, originally introduced by Bertolini–Darmon–Prasanna for modular curves in Bertolini et al. (Duke Math J 162(6):1033–1148, 2013), in the context of Mumford curves. The main result of this paper relates generalized Heegner cycles with the two variable anticyclotomic p-adic L-function attached to a Coleman family f∞ and an imaginary quadratic field K, constructed in Bertolini and Darmon (Invent Math 168(2):371–431, 2007) and Seveso (J Reine Angew Math 686:111–148, 2014). While in Bertolini and Darmon (Invent Math 168(2):371–431, 2007) and Seveso (J Reine Angew Math 686:111–148, 2014) only the restriction to the central critical line of this 2 variable p-adic L-function is considered, our generalised Heegner cycles allow us to study the restriction of this function to non-central critical lines. The main result expresses the derivative along the weight variable of this anticyclotomic p-adic L-function restricted to non necessarily central critical lines as a combination of the image of generalized Heegner cycles under a p-adic Abel–Jacobi map. In studying generalised Heegner cycles in the context of Mumford curves, we also obtain an extension of a result of Masdeu (Compos Math 148(4):1003–1032, 2012) for the (one variable) anticyclotomic p-adic L-function of a modular form f and K at non-central critical integers
Extensions of degree p4of a p-adic field
No full textLet K be a p-adic field. Restricting to the case of no intermediate extensions, we obtain formulae counting the number of (totally and wildly) ramified extensions of degree p(4) of K up to K-isomorphism and in particular, we count the number of isomorphism classes of extensions for which the Galois closure has a prescribed Galois group. The principal tool used is a result, proved in Del Corso et al. (On wild extensions of a p-adic field, arXiv:1601.05939v1), which states that there is a one-to-one correspondence between the isomorphism classes of extensions of degree p(k) of K having no intermediate extensions and the irreducible H-sub-modules of dimension k of F*/F*(p), where F is the composite of certain fixed normal extensions of K and H is its Galois group over K
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
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
- …
