Mathematical Sciences: L-Functions Associated to Siegel Modular 3-Folds

在这项研究中，奈加德将研究伽罗瓦表示 Siegel模形式的程度2和重量3，首先在 4级的特殊情况，但希望以后更多 一般性。 动机发生在Siegel的上同调中 模块化的品种，但暴露在上同调的一些多 简单的三折。 这三重是用θ函数构造的 黎曼公式和是简单的完全相交 二次曲面 由于这些动机的存在，我们 在Hasse-Weil Zeta中找到Andrianov L函数作为因子 Siegel modular 3-fold的函数。 模形式是对数进行编码的解析函数 理论上的信息，使研究人员能够使用深 分析工具来解决数论函数。 在这 研究代数几何中物体的模形式 进一步丰富了这项技术。 私家侦探构成了一些非常令人兴奋 他的努力一定会成功的。

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.