1,720,956 research outputs found
-adic equidistribution and an application to -units
Get PDFWe prove a Galois equidistribution result for torsion points in in the -adic setting for test functions of the form where is a nonzero polynomial with coefficients in the -adic numbers. Our result includes a power saving quantitative estimate of the decay rate rate of the equidistribution. As an application we show that Ih\u27s Conjecture is true for a class of divisors of .Comments are welcom
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe 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
Logarithmic equidistribution and other problems involving torsion points of the algebraic torus
Get PDFOne main result of this thesis is the proof of a conjecture of Ih for a certain class of polynomials. Let be a finite set of primes. The conjecture states that, if is a Lautrent polynomial over a number field in variables, then the set of torsion points of the -dimensional algebraic torus , such that is an -unit is not dense in , unless the zero set of is a finite union of torsion cosets.
As main tools we use equidistribution theorems in the archimedean setting and for all places above primes in . In the first case we use a recent result of Dimitrov and Habegger and with the same method we prove the analog statements in the -adic case. Since the Theorem of Tate and Voloch is crucial here, we tried to understand how the size of the constant depends on the height of the coefficients if all of them are algebraic.
We also had a look at other problems of logarithmic equidistribution. A very specific one is considered for -extensions of elliptic curves which admit a maximal compact subgroup . The function we look at is the logarithm of the absolute value of a coordinate of the embedding of into found by Masser using results of Serre. We show that the average over the Galois orbit of a torsion point of the evaluation of tends to the integral over with respect to the Haar measure as the order of the torsion point tends to infinity.
Further we consider the function on the complex plane, where is an algebraic number on the unit circle which is not a root of unity. Instead of considering roots of unity, we work with strict sequences of algebraic numbers whose height tends to zero. The question is, whether the conclusion of Bilu's equidistribution theorem is true in this case. We can show that the answer is no using results about simultaneous approximation. The question has a natural -adic analogue, which is proved in a similar way.
In another chapter we describe all sums of at most four roots of unity which add to an algebraic unit. The main trick is due to Dimitrov and uses Kronecker's theorem to translate the condition of being a unit to a necessary condition given by an equation.
Finally, we count torsion points in algebraic subvarieties of the algebraic torus. We estimate the growth rate of the number of torsion points of order bounded by as tends to infinity. There is a general bound which is sharp. If the algebraic subvariety does not contain a torsion coset of maximal dimension we get a power saving improvement of the general bound. The main tools are the theorems of Minkowski
Counting torsion points on subvarieties of the algebraic torus
Get PDFWe estimate the growth rate of the function which counts the number of
torsion points of order at most on an algebraic subvariety of the algebraic
torus over some algebraically closed field. We prove a general
upper bound which is sharp, and characterize the subvarieties for which the
growth rate is maximal. For all other subvarieties there is a better bound
which is power saving compared to the general one. Our result includes
asymptotic formulas in characteristic zero where we use Laurent's Theorem, the
Manin-Mumford Conjecture. However, we also obtain new upper bounds for the
algebraic closure of a finite field.Comment: Comments welcom
A note on logarithmic equidistribution
Get PDFFor every algebraic number on the unit circle which is not a root of
unity we prove the existence of a strict sequence of algebraic numbers whose
height tends to zero, such that the averages of the evaluation of
in the conjugates are essentially bounded from
above by . This completes a characterisation on functions
initiated by Autissier and Baker-Masser, who cover the cases
and respectively. Using the same ideas we also prove
analogues in the -adic setting.Comment: Comments welcom
Variations on the Author
Get PDF“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
Get PDFWe 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
Get PDFWe 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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