Mathematical Sciences: Arithmetic of Polynomials and Theta Functions

首席调查员将继续他关于当地和全球复杂权力的工作，此外，他还将继续他关于所谓伊古萨当地Zeta函数和Zeta分布的工作。他将专注于非齐次情形，它本身很有趣，人们可以从中推导出尖锐的猜想。我们还将学习theta函数的理论。研究了在代数几何算术理论中具有重要意义的特殊类型的Zeta函数。确定与局部因子相关的多项式将受到特别关注。还将讨论这些函数的极点的收敛、解析延拓和分布。

The Principal Investigator will continue his work on complex powers, both local and global, and, in addition, continue his work on the so-called Igusa local zeta functions and zeta distributions. He will concentrate on the prehomogeneous case, which is interesting in itself and from which one can formulate sharp conjectures. The theory of theta functions will also be looked at. The author studies special kinds of zeta functions which have importance in the arithmetic theory of algebraic geometry. Determining the polynomials associated to the local factors will receive special attention. Also discussed will be the convergence, analytic continuation and distribution of the poles of these functions.