代数K-理论领域著名的Beilinson 猜想将代数K-群的正规化子的值与L-函数的特殊值联系了起来, 深刻地揭示了代数K理论的算术意义. 由于代数 K-群结构的复杂性, 使得这方面的研究非常困难. 我们这个研究项目计划利用近年来的一些突破将正规化子的值转化为Mahler测度的值, 而Mahler 测度的值在很多情况下又能被超几何函数表示, 这为Beilinson 猜想领域的研究开辟了新的思路. 我们将利用模函数, 爱森斯坦级数等算术对象研究代数K-理论, Mahler测度与L-函数的特殊值之间的深刻联系, 解决特定情形下的Beilinson-猜想.

The famous Beilinson's Conjecture connects the values of Regulators and the special values of L-functions, reveal the deep arithmetic content of .algebraic K-theory. The research of these problems are very difficult due to the complexity of the structure of algebraic K-groups. We plan to use the recent breakthrough to transform the values of regulators to Mahler measures. Since the Mahler measures can be represented by hypergeometric functions in many cases, this will provide new ideas on the study of Beilinson's Conjecture. We will use arithmetic objects suc as modular function, Eisenstein series to study the connections among algebraic K-theory, Mahler measure and special values of L-functions and to solve some special problems on Beilinson' Conjecture.