Transcendental Numbers and Special Analytic Functions

DMS-0340812 Papanikolas，Matthew A.摘要：题目：超越数和特殊解析函数研究者提出了关于超越数和解析函数特殊值的几个问题，以理解解析量和算术量之间的许多联系。 在一个项目中，本研究探讨了由Anderson-Drinfeldmotives产生的具有正特征的数的性质，如周期和周期，特别关注Carlitz周期之间的代数关系。 此外，与N. Ramachandran博士的研究计划是研究交换簇的扩张群与HeckeL-函数和Rankin-SelbergL-函数的特殊值之间的关系。数论是现代数学的基本分支之一，是密码学和编码理论等许多应用的基础。 拟议的研究涉及数论的算术和分析方面之间的相互作用的问题，这在欧拉和高斯的经典著作中有其开端。 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.