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.

Computations of Vector-Valued Siegel Modular Forms

We carry out some computations of vector-valued Siegel modular forms of degree two, weight (k, 2) and level one, and highlight three experimental results: (1) we identify a rational eigenform in a three-dimensional space of cusp forms; (2) we observe that non-cuspidal eigenforms of level one are not always rational; (3) we verify a number of cases of conjectures about congruences between classical modular forms and Siegel modular forms. Our approach is based on Satoh's description of the module of vector-valued Siegel modular forms of weight (k, 2) and an explicit description of the Hecke action on Fourier expansions. (C) 2013 Elsevier Inc. All rights reserved.

Verifying Harder's Conjecture for Classical and Siegel Modular Forms

A conjecture by Harder shows a surprising congruence between the coefficients of “classical” modular forms and the Hecke eigenvalues of corresponding Siegel modular forms, contigent upon “large primes” dividing the critical values of the given classical modular form. Harder’s Conjecture has already been verified for one-dimensional spaces of classical and Siegel modular forms (along with some two-dimensional cases), and for primes p 37. We verify the conjecture for higher-dimensional spaces, and up to a comparable prime p.

Zeros of Weakly Holomorphic Modular Forms of Levels 2 and 3

Let M-k(#)(N) be the space of weakly holomorphic modular forms for Gamma(0)(N) that are holomorphic at all cusps except possibly at infinity. We study a canonical basis for M-k(#)(2) and M-k(#)(3) and prove that almost all modular forms in this basis have the property that the majority of their zeros in a fundamental domain lie on a lower boundary arc of the fundamental domain.

Survey Article: Characterizations of the Saito-Kurokawa Lifting

There are a variety of characterizations of Saito-Kurokawa lifts from elliptic modular forms to Siegel modular forms of degree 2. In addition to giving a survey of known characterizations, we apply a recent result of Weissauer to provide a number of new and simpler characterizations of Saito-Kurokawa lifts.

Crystallization of Escherichia coli Catabolite Gene Activator Protein with its DNA Binding Site: The use of Modular DNA

To obtain crystals of the Escherichia coli catabolite gene activator protein (CAP) complexed with its DNA-binding site, we have searched for crystallization conditions with 26 different DNA segments ≥28 base-pairs in length that explore a variety of nucleotide sequences, lengths, and extended 5′ or 3′ termini. In addition to utilizing uninterrupted asymmetric lac site sequences, we devised a novel approach of synthesizing half-sites that allowed us to efficiently generate symmetric DNA segments with a wide variety of extended termini and lengths in the large size range (≥28 bp) required by this protein. We report three crystal forms that are suitable for X-ray analysis, one of which (crystal form III) gives measurable diffraction amplitudes to 3 Å resolution. Additives such as calcium, n-octyl-β-d-glucopyranoside and spermine produce modest improvements in the quality of diffraction from crystal form III. Adequate stabilization of crystal form III is unexpectedly complex, requiring a greater than tenfold reduction in the salt concentration followed by addition of 2-methyl-2,4-pentanediol and then an increase in the concentration of polyethylene glycol.

The co-evolution of development needs and IOR forms: development by committee in Bosnia

This work highlights opportunities and obstacles to success in four task forces typically found at different times in states of conflict, transition, and development. They include: refugee return, media issues, privatization of state-owned enterprises, and efforts to promote business development. Based on over 180 in-depth interviews and observations of dozens of meetings during five lengthy field research trips to the Bosnian region between 1999 and 2005, this manuscript analyzes how these four task forces differed in terms of context, strategy, organization, and management in an attempt to understand the co-evolution of international development needs and the interorganizational forms that address them.

"Framing Counterspaces: Forms and Meanings of Graffiti in Berlin's Linguistic Landscape"

Street art and graffiti are integral parts of Berlin’s urban space, which has undergone dramatic transformations in the past two decades. Graffiti texts constitute a critical comment on these urban transformations. This talk analyzes the connection between the phenomenon of street art and trajectories in urban planning in post-wall Berlin. My current research explores the meaning of various forms of street art (such as graffiti, posters, sticker art, stencils) as texts in Berlin’s linguistic landscape. Linguistic Landscape research pays critical attention to language, words, and images displayed and exposed in public spaces. The field of Linguistic Landscapes has only recently begun to include graffiti texts in analyses of text and space to fully comprehend the semiotics of the street. In the case of Germany’s capital, graffiti writing enters into a critical dialogue with the environment and provides a readable text to understand the city.

Pond-Women Revelations: The Subaltern Registers in Maithil Women's Expressive Forms

Ponds are ubiquitous in the Maithil region of Nepal, and they figure prominently in folk narratives and ceremonial paintings produced by women there. I argue that in Maithil women's folktales, as in their paintings, the trope of ponds shifts the imaginative register toward women's perspectives and the importance of women's knowledge and influence in shaping Maithil society, even as this register shift occurs within plots featuring male protagonists. I argue further that in the absence of a habit of exegesis in their expressive arts, and given the cross-referential, dialogic nature of expressive practices, a methodology that draws into interpretive conversation the multitude of expressive forms exercised by Maithil women enhances analytical access to Maithil women's collective perspectives on their social and cosmological worlds.

Plato's Doctrine Of Forms: Modern Misunderstandings

Among the philosophical ideas of Plato, perhaps the most famous is his doctrine of forms. This doctrine has faced harsh criticism due, in large part, to the interpretations of this position by modern philosophers such as René Descartes, John Locke, and Immanuel Kant. For example, Plato has been interpreted as presenting a ¿two-worlds¿ approach to form and thing and as advancing a rationalist approach to epistemology. His forms have often been interpreted as ideas and as perfect copies of the things of the visible world. In this thesis, I argue that these, along with other interpretations of Plato presented by the moderns, are based on misunderstandings of Plato¿s overall philosophy. In so doing, I attempt to show that the doctrine of forms cannot be directly interpreted into the language of Cartesian, Lockean, and Kantian metaphysics and epistemology, and thus should not be prematurely dismissed because of these modern Platonic interpretations. By analyzing the Platonic dialogues beside the writings of the modern philosophers, I conclude that three of the most prominent modern philosophers, as representatives of their respective philosophical frameworks, have fundamentally misunderstood the nature of Plato¿s famous doctrine of forms. This could have significant implications for the future of metaphysics and epistemology by providing an interpretation of Plato which adds to, instead of contradicts, the developments of modern philosophy.