1,720,962 research outputs found
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
On the geometry of the Humbert surface of square discriminant
Full text linkFor every positive integer we determine the Enriques--Kodaira type of the Humbert surface of discriminant which parametrises principally polarised abelian surfaces that are -isogenous to a product of elliptic curves. A key step in the proof is to analyse the fixed point locus of a Fricke-like involution on the Hilbert modular surface of discriminant which was studied by Hermann and by Kani and Schanz. To this end, we construct certain diagonal Hirzebruch--Zagier divisors which are fixed by this involution. In our analysis we obtain a genus formula for these divisors, which includes the case of modular curves associated to (any) extended Cartan subgroup of and which may be of independent interest.66 pages, 18 figure
On -congruences of elliptic curves
Full text linkWe construct infinite families of pairs of (geometrically non-isogenous)
elliptic curves defined over with -torsion subgroups that are
isomorphic as Galois modules. This extends previous work of Chen and Fisher
where it is assumed that the underlying isomorphism of -torsion subgroups
respects the Weil pairing. Our approach is to compute explicit birational
models for the modular diagonal quotient surfaces which parametrise such pairs
of elliptic curves.
A key ingredient in the proof is to construct simple (algebraic) conditions
for the , , or -torsion subgroups of a pair of elliptic curves to be
isomorphic as Galois modules. These conditions are given in terms of the
-invariants of the pair of elliptic curves.Comment: 26 pages. Minor corrections and clarifications, especially Section
Congruences of elliptic curves arising from non-surjective mod Galois representations
Full text linkWe study -congruences between quadratic twists of elliptic curves. If
has exactly two distinct prime factors we show that these are parametrised by
double covers of certain modular curves. In many, but not all cases, the
modular curves in question correspond to the normaliser of a Cartan subgroup of
. By computing explicit models for these
double covers we find all pairs such that there exist infinitely many
-invariants of elliptic curves which are -congruent with
power to a quadratic twist of . We also find an example of a
-congruence over . We make a conjecture classifying nontrivial
-congruences between quadratic twists of elliptic curves over
.
Finally, we give a more detailed analysis of the level case. We use
elliptic Chabauty to determine the rational points on a modular curve of genus
whose Jacobian has rank and which arises as a double cover of the
modular curve . As a consequence we obtain
a new proof of the class number problem.Comment: 33 pages. Clarified the proof of Proposition 4.2 and minor
correction
Explicit -torsion in the Tate-Shafarevich groups of genus Jacobians
Full text linkWe describe an algorithm which, on input a genus curve
whose Jacobian has real multiplication by a quadratic order in
which splits, outputs twists of the Klein quartic curve parametrising
elliptic curves whose mod Galois representations are isomorphic to a
sub-representation of the mod Galois representation attached to
. Applying this algorithm to genus curves of small conductor
in families of Bending and Elkies--Kumar we exhibit a number of genus
Jacobians whose Tate--Shafarevich groups (unconditionally) contain a
non-trivial element of order which is visible in an abelian three-fold.Comment: 12 pages; an example constructed in this paper has appeared in the
appendix to arXiv:2312.0730
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
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