1,720,961 research outputs found
Equations and rational points of the modular curves X_0^+(p)
No full textLet p be an odd prime number and let X+0 (p) be the quotient of the classical modular curve X0(p) by the action of the Atkin-Lehner operator wp. In this paper we show how to compute explicit equations for the canonical model of X+0 (p). Then we show how to compute the modular parametrization, when it exists, from X+0 (p) to an isogeny factor E of dimension 1 of its jacobian J+0 (p). Finally, we show how use this map to determine the rational points on X+0 (p) up to a large fixed height
Classification of algebraic function fields with class number one
Get PDFIn this paper we prove that there are exactly eight function fields, up to isomorphism, over finite fields with class number one and positive genus. This classification was already suggested, although not completely proved, in a previous work about this topic
Intersection matrices for the minimal regular model of X0(N) and applications to the Arakelov canonical sheaf
No full textLet N>1 be an integer coprime to such that and let be the genus of the modular curve . We compute the intersection matrices relative to special fibres of the minimal regular model of . Moreover we prove that the self-intersection of the Arakelov canonical sheaf of is asymptotic to , for
Rational Points on Modular Curves
Get PDFI explain a way to compute Fourier coefficients of modular forms associated to normalizer of non-split Cartan subgroups of GL(2,Z/pZ) and how, using these coefficients, one can compute explicit equations of modular curves associated to same subgroup. I attached some tables containing some examples of results of this method
Modular Curves with many Points over Finite Fields
Get PDFWe describe an algorithm to compute the number of points over finite fields
on a broad class of modular curves: we consider quotients for a
subgroup of \GL_2(\mathbb Z/n\mathbb Z) such that for each prime dividing
, the subgroup at is either a Borel subroup, a Cartan subgroup, or
the normalizer of a Cartan subgroup of \GL_2(\mathbb Z/p^e\mathbb Z), and for
any subgroup of the Atkin-Lehner involutions of . We applied our
algorithm to more than ten thousands curves of genus up to 50, finding more
than one hundred record-breaking curves, namely curves X/\FF_q with genus
that improve the previously known lower bound for the maximum number of points
over \FF_q of a curve with genus . As a key technical tool for our
computations, we prove the generalization of Chen's isogeny to all the Cartan
modular curves of composite level
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
Automorphisms of Cartan modular curves of prime and composite level
Get PDFWe study the automorphisms of modular curves associated to Cartan subgroups
of and certain subgroups of their
normalizers. We prove that if is large enough, all the automorphisms are
induced by the ramified covering of the complex upper half-plane. We get new
results for non-split curves of prime level : the curve
has no non-trivial automorphisms, whereas the curve
has exactly one non-trivial automorphism. Moreover, as an
immediate consequence of our results we compute the automorphism group of
, where is the group generated by the Atkin-Lehner
involutions of and is a large enough square.Comment: 36 pages, 4 tables. Some proofs rely on MAGMA scripts available at
https://github.com/guidoshore/automorphisms_of_Cartan_modular_curve
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