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David Roberts
No full textRoberts, David P.; Rodriguez Villegas, Fernando; Hypergeometric motives. Notices Amer. Math. Soc. 69(2022), no. 6, 914–929https://digitalcommons.morris.umn.edu/cosa2022/1028/thumbnail.jp
The structure of bivariate rational hypergeometric functions
Get PDFWe describe the structure of all codimension-2 lattice configurations A which admit a stable rational A-hypergeometric function, that is a rational function F all the partial derivatives of which are nonzero, and which is a solution of the A-hypergeometric system of partial differential equations defined by Gel′ fand, Kapranov, and Zelevinsky. We show, moreover, that all stable rational A-hypergeometric functions may be described by toric residues and apply our results to study the rationality of bivariate series the coefficients of which are quotients of factorials of linear forms.Fil: Cattani, Eduardo. University Of Massachussets; Estados UnidosFil: Dickenstein, Alicia Marcela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Rodriguez Villegas, Fernando. University of Texas at Austin; Estados Unido
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
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Some applications of classical modular forms to number theory
Get PDFIn this thesis we use classical modular forms to study several problems in
number theory. In chapter 2 we use non-holomorphic Eisenstein series for the Hilbert
modular group to obtain a formula for the relative class number of certain abelian
extensions of CM number fields. In chapter 3 we compute the scattering determinant for the Hilbert modular group, and explain how this can be used to prove
that the subspace of cuspidal, square integrable eigenfunctions for the Laplacian on
products of rank one symmetric spaces is infinite dimensional. In chapter 4 we use
zeta functions of quadratic forms over number fields to sharpen a certain constant
appearing in C. L. Siegel’s lower bound for the residue of the Dedekind zeta function
at s = 1.Mathematic
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The Brandt module of ternary quadratic lattices
Get PDFtextGiven a positive definite ternary quadratic lattice Λ, we construct
a free module M(Λ) with Hecke action, together with a family of
Hecke-linear maps ϑl from M(Λ) to certain spaces of modular forms
of half integral weight. The latter are given explicitly by a new kind
of generalized theta series, which we prove to be modular with level
independent of l. Key to our work is the introduction of a refinement
to the classic notion of proper equivalence of lattices.Mathematic
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Some relations of Mahler measure with hyperbolic volumes and special values of L-functions
Get PDFtextWe construct families of polynomials of up to five variables whose Mahler measures
are given in terms of multiple polylogarithms. The formulas are homogeneous and
their weight coincides with the number of variables of the corresponding polynomial.
Next, we fix the coefficients of these families and find some n-variable polynomial
families whose Mahler measure is expressed in terms of polylogarithms, zeta functions,
and Dirichlet L-functions.
We also develop examples of formulas where the Mahler measure of certain
polynomial may be interpreted as the volume of a hyperbolic object.
The examples involving polylogarithms, zeta functions and Dirichlet L-functions
are expected to be related to computations of regulators in motivic cohomology as
observed by Deninger, and later Rodriguez-Villegas and Maillot. While RodriguezVillegas
made this relationship explicit for the two variable case, we have described
in detail the three variable case and we expect to extend our ideas to several variables.Mathematic
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Evaluations of multiple L-values
Get PDFtextIn this paper, the methods of D. Zagier, J. Borwein, and R. Girgensohn
for proving evaluations of multiple zeta values are generalized to the case of
the multiple L-values. Numerical computation of these numbers based on
the method of Crandall is also demonstrated.Mathematic
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
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