Numerical Computation of a Certain Dirichlet Series Attached to Siegel Modular Forms of Degree Two

The Rankin convolution type Dirichlet series D-F,D-G(s) of Siegel modular forms F and G of degree two, which was introduced by Kohnen and the second author, is computed numerically for various F and G. In particular, we prove that the series D-F,D-G(s), which shares the same functional equation and analytic behavior with the spinor L-functions of eigenforms of the same weight are not linear combinations of those. In order to conduct these experiments a numerical method to compute the Petersson scalar products of Jacobi Forms is developed and discussed in detail.

America's Shifting Color Line? Reexamining Determinants of Latino Racial Self-Identification

Objectives. Latinos are the nation's largest minority group and will double in size by 2050. Their size coupled with the fact that Latinos do not constitute a separate race raises questions about Latinos' incorporation into the U. S. racial hierarchy. This article explores patterns of Latino racial identity formation, examining the determinants of racial identity. Methods. Using the 2006 Latino National Survey, I estimate multinomial logit and ordered probit models of identification choices. Results. Latino racial identity is strongly associated with several factors, including socioeconomic status, measures of perceived discrimination and commonality, and measures of acculturation/assimilation. Most Latinos have a broader, more complex understanding of race. Furthermore, some Latinos do believe that they occupy a unique position in the racial hierarchy. Conclusions. The results suggest that the color line W. E. DuBois argued has long divided our nation may eventually shift.

Pervasive Algebras and Maximal Subalgebras.

A uniform algebra A on its Shilov boundary X is maximal if A is not C(X) and no uniform algebra is strictly contained between A and C(X) . It is essentially pervasive if A is dense in C(F) whenever F is a proper closed subset of the essential set of A. If A is maximal, then it is essentially pervasive and proper. We explore the gap between these two concepts. We show: (1) If A is pervasive and proper, and has a nonconstant unimodular element, then A contains an infinite descending chain of pervasive subalgebras on X . (2) It is possible to find a compact Hausdorff space X such that there is an isomorphic copy of the lattice of all subsets of N in the family of pervasive subalgebras of C(X). (3) In the other direction, if A is strongly logmodular, proper and pervasive, then it is maximal. (4) This fails if the word “strongly” is removed. We discuss examples involving Dirichlet algebras, A(U) algebras, Douglas algebras, and subalgebras of H∞(D), and develop new results that relate pervasiveness, maximality, and relative maximality to support sets of representing measures.

The Fundamental Gap For Hyperbolic Triangles

In 1983, M. van den Berg made his Fundamental Gap Conjecture about the difference between the first two Dirichlet eigenvalues (the fundamental gap) of any convex domain in the Euclidean plane. Recently, progress has been made in the case where the domains are polygons and, in particular, triangles. We examine the conjecture for triangles in hyperbolic geometry, though we seek an for an upper bound for the fundamental gap rather than a lower bound.

Rates Of Obesity And Incidence Of Diabetes In Hispanics In The United States: An Examination Of The Epidemiological Paradox

Using pooled data from the 2008-2011 National Health Interview Survey and employing multinomial and binomial logistic regression methods, this research examines disparities in rates of obesity and incidence of diabetes between individual Hispanic subgroups in comparison to non-Hispanic whites and blacks. Immigration status(including nativity, duration in the United States, and citizenship status) is hypothesized to play a central role in rates and obesity and incidence of diabetes. Unlike Cuban-Americans, Mexican-Americans, Puerto Ricans, and other Hispanics were more likely to be overweight as well as obese when compared to non-Hispanic whites. Mexican-Americans had the only significance in prevalence of type 2 diabetes in comparison to non-Hispanic whites. Both of these health outcomes are strongly associated with the various immigration variables.

Isospectrality and Heat Content

We present examples of isospectral operators that do not have the same heat content. Several of these examples are planar polygons that are isospectral for the Laplace operator with Dirichlet boundary conditions. These include examples with infinitely many components. Other planar examples have mixed Dirichlet and Neumann boundary conditions. We also consider Schrodinger operators acting in L-2[0,1] with Dirichlet boundary conditions, and show that an abundance of isospectral deformations do not preserve the heat content.