1,720,965 research outputs found
Growth of the analytic rank of modular elliptic curves over quintic extensions
No full textGiven F a totally real number field and E/F a modular elliptic curve, we denote by G5(E/F; X) the number of quintic extensions K of F such that the norm of the relative discriminant is at most X and the analytic rank of E grows over K, i.e., ran(E/K) > ran(E/F). We show that G5(E/F; X) +∞ X when the elliptic curve E/F has odd conductor and at least one prime of multiplicative reduction. As Bhargava, Shankar and Wang [1] showed that the number of quintic extensions of F with norm of the relative discriminant at most X is asymptotic to c5,FX for some positive constant c5,F, our result exposes the growth of the analytic rank as a very common circumstance over quintic extensions
Plectic Stark–Heegner points
No full textWe propose a conjectural construction of determinants of global points on modular elliptic curves over arbitrary number fields, generalizing both the p-adic construction of Heegner points via Čerednik–Drinfeld uniformization and the definition of classical Stark–Heegner points. In alignment with Nekovář and Scholl's plectic conjectures, we expect the non-triviality of these plectic Stark–Heegner points to control the Mordell–Weil group of higher rank elliptic curves. We provide some indirect evidence for our conjectures by showing that higher order derivatives of anticyclotomic p-adic L-functions compute plectic invariants
On the algebraicity of polyquadratic Plectic Points
No full textWe establish direct evidence of the arithmetic significance of plectic Stark–Heegner points for elliptic curves of arbitrarily large rank. The main contribution is a proof of the algebraicity of plectic points associated to polyquadratic CM extensions of totally real number fields. Moreover, we relate the non-vanishing of plectic points to analytic and algebraic ranks of elliptic curves
Hirzebruch–Zagier classes and rational elliptic curves over quintic fields
No full textConditionally on a conjecture on the étale cohomology of Hilbert modular surfaces and some minor technical assumptions, we establish new instances of the equivariant BSD-conjecture in rank 0 with applications to the arithmetic of rational elliptic curves over quintic fields. The key ingredients are a refinement of twisted triple product p-adic L-functions, the construction of a compatible collection of Hirzebruch–Zagier cycles and an explicit reciprocity law relating the two
Twisted triple product p-adic L-functions and Hirzebruch-Zagier cycles
No full textLet L/F be a quadratic extension of totally real number fields. For any prime unramified in L, we construct a p-adic L-function interpolating the central values of the twisted triple product L-functions attached to a p-nearly ordinary family of unitary cuspidal automorphic representations of GL_{2,L\times F}. Furthermore, when L is a real quadratic number field and p is a split prime, we prove a p-adic Gross-Zagier formula relating the values of the p-adic L-function outside the range of interpolation to the syntomic Abel-Jacobi image of generalized Hirzebruch-Zagier cycles
Plectic p-adic invariants
No full textFor modular elliptic curves over number fields of narrow class number one, and with multiplicative reduction at a collection of p-adic primes, we define new p-adic invariants. Inspired by Nekovář and Scholl's plectic conjectures, we believe these invariants control the Mordell–Weil group of higher rank elliptic curves and we support our expectations with numerical experiments
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
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