In this research Nygaard will study Galois representations of Siegel modular forms of degree 2 and weights 3, at first in the special case of level 4 but hopefully later on in more generality. The motives occur in the cohomology of Siegel modular varieties but are exposed in the cohomology of some much simpler 3-folds. These 3-folds are constructed using the theta formulas of Riemann and are simple complete intersections of quadrics. As a consequence of the existence of these motives we find Andrianov L-functions as factors in the Hasse-Weil Zeta function of the Siegel modular 3-fold. Modular forms are analytic functions which encode number theoretic information allowing the researcher to use the deep tools of analysis to solve number theoretic functions. In this research modular forms attached to objects in algebraic geometry further enrich this technique. The P.I. poses some very exciting problems and will surely be successful in his endeavors.
