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A weighted one-level density of families of L-functions
No full textThis paper is devoted to a weighted version of the one-level density of the nontrivial zeros of L-functions, tilted by a power of the L-function evaluated at the central point. Assuming the Riemann hypothesis and the ratio conjecture, for some specific families of L-functions, we prove that the same structure suggested by the density conjecture also holds in this weighted investigation, if the exponent of the weight is small enough. Moreover, we speculate about the general case, conjecturing explicit formulae for the weighted kernels
Weighted statistics of L-functions
No full textThis thesis consists of four chapters.
Chapter 1 and 2 are a general introduction to the Riemann zeta function, with a special focus on the theory of moments; no original results are contained here.
In Chapter 3 we study a weighted value distribution of the Riemann zeta function on the critical line. More specifically, assuming the Riemann Hypothesis, we investigate the distribution of with respect to various tilted measures, proving several weighted analogues of Selberg's central limit theorem. Moreover we prove unconditionally the analogue results in the corresponding random matrix theory setting. These contents first appeared in [54,55].
Chapter 4 is devoted to a weighted version of the one-level density of the non-trivial zeros of -functions, tilted by a power of the -function evaluated at the central point. First, we study this problem for the Riemann zeta function, both unconditionally and assuming the ratio conjecture. Then we generalize these ideas for specific families of -functions with different symmetry types; in particular we consider a symplectic and an orthogonal family of -functions and, under the relevant ratio conjecture, we study the weighted one-level density of non-trivial zeros of these -functions
A weighted one-level density of the non-trivial zeros of the Riemann zeta-function
No full textWe compute the one-level density of the non-trivial zeros of the Riemann zeta-function weighted by |ζ(12+it)|2k for k=1 and, for test functions with Fourier support in (-12,12), for k=2. As a consequence, for k=1,2, we deduce under the Riemann hypothesis that T(logT)[email protected]@4abf1d3bkjavax.xml.bind.JAXBElement@5508e36djavax.xml.bind.JAXBElement@2bd394ebjavax.xml.bind.JAXBElement@52d251f1javax.xml.bind.JAXBElement@6036c855 non-trivial zeros of ζ, of imaginary parts up to T, are such that ζ attains a value of size (logT)k+o(1) at a point which is within O(1/logT) from the zero
Consecutive real quadratic fields with large class numbers
No full textFor a given positive integer , we prove that there are at least
integers such that the real quadratic fields have class numbers essentially as
large as possible.Comment: 7 pages; strengthened the results and added a co-author; comments are
welcome
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
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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