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.

Government Influence and the Failure of Fannie Mae and Freddie Mac

In 2008 two government-sponsored enterprises, Fannie Mae and Freddie Mac, were placed into conservatorship due to insolvency. The financial bailout of the two publically traded corporations came at the expense of the American tax payer. This study investigates the relationship between direct and indirect government influence and the increasing risk taking of Fannie Mae and Freddie Mac from the late 1990’s through their conservatorship in 2008. As government-sponsored enterprises Fannie Mae and Freddie Mac have many special advantages that other publically traded companies did not possess. These advantages allowed Fannie Mae and Freddie Mac to increase their profitability. Theoretical literature regarding Congress and the bureaucracy suggests that the actions of bureaucrats can be linked to the preferences of Congressional members because bureaucrats are responsive to potential threats or perceived threats from the legislature. This theory is applicable to Fannie Mae and Freddie Mac, and is used to explain why the government was able to directly and indirectly influence the government-sponsored enterprises. Overall this investigation has determined that the United States government pursued a clear mission that determined to increase the availability of housing to all Americans, specifically to low-income and under-served individuals, through the use of the government-sponsored enterprises. Despite this link there is no conclusive data to show that the pursuit of this housing mission led Fannie Mae and Freddie Mac to operate in riskier business segments. This study has also found that motivation regarding profit-seeking and compensation structure provide a more plausible explanation for why the government-sponsored enterprises began to engage in riskier business practices that led to their insolvency.

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.