Anderson–Ihara Theory: Gauss Sums and Circular Units
Anderson–Ihara Theory: Gauss Sums and Circular Units
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安德森-伊原理论：高斯和与圆单位
DOI：
10.2969/aspm/01710055
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发表时间：
1989
影响因子：
1.7
通讯作者：
R. Coleman
中科院分区：
文献类型：
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作者：
R. Coleman
几年前，Ihara, [I] 发现了一种新的幂级数，与 Ga 对 /-幂次费马曲线 Tate 模的作用有关。从那时起，Anderson, [A] 完善并概括了这些幂级数，将它们解释为经典 beta 函数的类似物。此外，一旦进行了这种类比，他自然就被迫将它们分解为三个“伽玛函数”的乘积。上一段故意含糊且过于简单化。在这篇文章中，我将尝试使其中的一些内容不再那么模糊，并指出这些“伽玛”和“贝塔”函数的理论如何与眼球切开术的其他方面联系起来并应用于其中。
A few years ago, Ihara, [I], discovered a new sort of power series connected with the action of Ga on the Tate-modules of Fermat curves of /-power degree. Since then Anderson, [A], refined and generalized these power series, interpreting them as analogues of the classical beta function. Moreover, once this analogy was made he naturally was forced to factor them into a product of three "gamma functions." The previous paragraph is purposely vague and oversimplified. In this article I will attempt to make some of it a little less vague and indicate how the theory of these "gamma" and "beta" functions may be connected with and applied to other aspects of cyclotomy.