魏福村 Fu-Tsun Wei

建立正特徵值的Kronecker極限式
在函數體之算術研究中取得重大進展

One of my research topics focuses on special values of the L-functions coming from automorphic forms over function fields. In the study of automorphic L-functions, Eisenstein series emerge as “kernel functions” and play essential roles in the Langlands program. My current pursuit involves exploring the arithmetic and geometric narratives hidden within the special values of Eisenstein series in positive characteristic.

The cornerstone of my seminal work is the derivation of a function field analogue of the Kronecker limit formula for Eisenstein series across arbitrary ranks. This formula, in the context of positive characteristic, was initially formulated for the rank 2 case in my earlier work. My breakthrough lies in extending the formula to arbitrary ranks through a more conceptual methodology. This comprehensive result was published in Inventiones Mathematicae, a leading journal in the field of mathematics. The formula enhances our understanding of Eisenstein series and enables direct applications to period interpretations of special L-values. Moreover, my collaboration with Professor Papikian from Penn State University uses this general formula to examine the cuspidor divisors of the Drinfeld modular varieties in arbitrary ranks, marking another significant contribution to my work. Numerous related projects are currently underway.