1,720,957 research outputs found
Growth of Fourier coefficients of vector-valued automorphic forms
No full texthttp://dx.doi.org/10.13039/501100000781 European Research Counci
Exponential sums in prime fields for modular forms
Full text linkThe main objective of this article is to study the exponential sumsassociated to Fourier coefficients of modular forms supported at numbers havinga fixed set of prime factors. This is achieved by establishing an improvementon Shparlinski's bound for exponential sums attached to certain recurrencesequences over finite fields.<br
The elliptic sieve and Brauer groups
Full text linkA theorem of Serre states that almost all plane conics over Q have no rational point. We prove an analogue of this for families of conics parametrised by elliptic curves using elliptic divisibility sequences and a version of the Selberg sieve for elliptic curves. We also give more general results for specialisations of Brauer groups, which yields applications to norm form equations
Lifting of vector-valued automorphic forms
Full text linkRecently, the first author [1] showed that the admissible vector-valued
automorphic forms lift to the admissible ones. In this article, we study the
lifts for the logarithmic vector-valued automorphic forms and explicitly
compute the Fourier coefficients of the lifted vector-valued automorphic forms.Comment: 20 pages, revised following referee's suggestion
Elliptic curves, modular forms, and the associated exponential sums
Full text linkThis thesis focuses on the various arithmetic aspects of elliptic curves and modular forms. Employing the exponential sum estimates obtained from sum-product estimates for finite fields, we estimate exponential sums linked to linear recurrence sequences and unveil additive characteristics of the Fourier coefficients of congruence modular forms. Additionally, we present a method for analyzing these additive properties through associated Galois representations of composite moduli. In exploring the non-congruence aspect, we delve into modular forms within vector-valued settings, analyze the growth patterns of Fourier coefficients, and evaluate their impact on corresponding exponential sums. Towards the end, we study character sums with elliptic sequences, leading to a better understanding of the elliptic Wieferich primes.2024-03-0
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
Watkins\u27s conjecture for elliptic curves with a rational torsion
Full text linkWatkins\u27s conjecture suggests that for an elliptic curve , the rank of the group of rational points is bounded above by , where is the modular degree associated with . It is known that Watkins\u27s conjecture holds on average. This article investigates the conjecture over certain thin families of elliptic curves. For example, for prime , we quantify the elliptic curves featuring a rational -torsion that satisfies Watkins\u27s conjecture. Additionally, the study extends to a broader context, investigating the inequality for any positive integer .26 pages; comments, and feedback are welcom
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