Zero of Special Functions

该奖项为两名在首席研究员的指导下从事数论问题研究的本科生提供资助。讨论了数域和代数曲线的l函数的根。黎曼函数是这种l函数中最著名的例子。了解树根的确切位置将产生深远的影响。例如，关于zeta函数的根的信息与素数的分布有关，而曲线的l函数的根与曲线上点的数量有关。学生们将学习一些具体的例子——由梅林变换产生的正交多项式。它们具有特别简单的形式，并且分析这些函数所需的背景不是扩展。使用Maple等软件进行符号计算将在这项工作中发挥重要作用。

This award provides support for two undergraduate researchers working under the supervision of the principal investigator on problems arising from number theory. It is concerned with the roots of L-functions of number fields and of algebraic curves. The Riemann zeta function is the most famous example of such an L-function. Knowledge of the precise location of the roots would have far reaching implications. For example, information on the roots of the zeta function relates to the distribution of prime numbers, while the roots of the L-function of a curve are related to the number of points on the curve. The students will study certain concrete cases - orthogonal polynomials which arise as Mellin transforms. They have a particularly simple form, and the background needed to analyze these functions is not extension. Symbolic computation using software such as Maple will play an important role in this work.