Transcendental Numbers and Special Analytic Functions

DMS-0340812 Papanikolas，Matthew A.摘要：标题：超越数与特殊解析函数为了了解解析量与算术量之间的诸多联系，作者提出了几个关于解析函数的超越数与特殊值的问题。在一个项目中，这项研究探索了由Anderson-Drinfeld动机产生的无正特征的数的性质，如周期和对数，并特别关注Carlitz对数之间的代数关系。此外，与N.Ramachandran合作，作者计划研究交换变种在数域上的扩张群与Heckel-函数和Rankin-Selberg L-函数的特定值之间的关系。作为现代数学的基本分支之一，数论是任何应用的基础，包括密码学和编码论。所提出的研究考虑了涉及数论的算术和分析方面之间的相互作用的问题，这些问题起源于欧拉和高斯的经典著作。该项目的几个部分自然会导致研究生和本科生研究的问题。

DMS-0340812Papanikolas, Matthew A.Abstract:Title: Transcendental numbers and special analytic functionsThe investigator proposes to work on severalproblems about transcendental numbers and specialvalues of analytic functions, in order tounderstand the many links between analytic andarithmetic quantities. In one project, thisresearch explores properties of numbers arising inpositive characteristic from Anderson-Drinfeldmotives, such as periods and logarithms, and inparticular focuses on the algebraic relationsamong Carlitz logarithms. Furthermore, incollaboration with N. Ramachandran, theinvestigator plans to study the relationshipsbetween extension groups of abelian varieties overnumber fields and special values of HeckeL-functions and Rankin-Selberg L-functions.One of the fundamental branches of modernmathematics, number theory serves as the basis formany applications, including cryptography andcoding theory. The proposed research considersquestions involving the interplay betweenarithmetic and analytic aspects of number theory,which have their beginnings in classical work ofEuler and Gauss. Several parts of the projectlead naturally to problems for graduate andundergraduate research.