Minimal Representations and Functoriality

摘要：SavinGordan萨文是继续他的工作，最低表示，与应用程序和明确的建设的一些情况下，朗兰兹functorality这不能得到任何其他方法。 自守形式是分析、代数和数论的交叉学科。这是一个植根于不可或缺的数学理论，如傅立叶分析，以多种方式影响我们的日常生活的主题。如果没有傅立叶分析，电信、数据传输和现代放射学仪器都是不可能的。本研究的目的是利用分析工具（微积分）来回答数论中的一些问题，例如更好地理解多项式的零点。几乎每个人都知道如何解一个二次方程。也有可能找到任何3或4次多项式的零点，尽管这一点鲜为人知。一般来说，高次多项式不能求解，但可以使用一些特殊的复变函数（称为模形式）来研究。 这个概念的循环，令人惊讶地将乍一看似乎并不相关的数学理论联系起来，大约有30年的历史，并被称为朗兰兹纲领，以普林斯顿高等科学研究所的罗伯特·P·朗兰兹命名。

Abstract: SavinGordan Savin is continuing his work on minimal representations, with applications to and explicit constructions of some cases of Langlands functoriality which can not be obtained by any other method. The subject of automorphic forms is a crossroad of analysis, algebra, and number theory. It is a subject with roots in indispensable mathematical theories such as Fourier Analysis which impact our everyday lives in many ways. Telecommunications, data transmission, and modern instruments of radiology would not be possible without Fourier Analysis. A purpose of this research is to use tools of analysis (calculus) to answer some questions in number theory, such as to get a better understanding of zeroes of polynomials. Almost everybody knows how to solve a quadratic equation. It is also possible, although it is less known, to find zeroes of any polynomial of degree 3 or 4. A higher degree polynomial, in general, cannot be solved, but can be studied using some special functions of complex variable (called modular forms). This circle of ideas, which surprisingly relates mathematical theories which at first glance do not appear related, is about 30 years old, and called the Langlands Program, after Robert P. Langlands of the Institute of Advanced Sciences in Princeton.