On the Cohomology of GL2 and SL2 over Imaginary Quadratic Fields

IF 0.7 4区数学 Q2 MATHEMATICS

Experimental Mathematics Pub Date : 2024-09-01 DOI:10.1080/10586458.2024.2379797

Herbert Gangl, Paul E. Gunnells, Jonathan Hanke, Dan Yasaki

引用次数: 0

Abstract

We report on computations of the cohomology of GL2(OD) and SL2(OD) , where D < 0 is a fundamental discriminant. These computations go well beyond earlier results of Vogtmann and Scheutzow. We us...

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论 GL2 和 SL2 在虚二次域上的同调性

我们报告了 GL2(OD) 和 SL2(OD) 的同调计算，其中 D < 0 是基本判别式。这些计算远远超出了沃格特曼和舍伊佐夫的早期结果。我们...

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来源期刊

Experimental Mathematics 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Experimental Mathematics publishes original papers featuring formal results inspired by experimentation, conjectures suggested by experiments, and data supporting significant hypotheses. Experiment has always been, and increasingly is, an important method of mathematical discovery. (Gauss declared that his way of arriving at mathematical truths was "through systematic experimentation.") Yet this tends to be concealed by the tradition of presenting only elegant, fully developed, and rigorous results. Experimental Mathematics was founded in the belief that theory and experiment feed on each other, and that the mathematical community stands to benefit from a more complete exposure to the experimental process. The early sharing of insights increases the possibility that they will lead to theorems: An interesting conjecture is often formulated by a researcher who lacks the techniques to formalize a proof, while those who have the techniques at their fingertips have been looking elsewhere. Even when the person who had the initial insight goes on to find a proof, a discussion of the heuristic process can be of help, or at least of interest, to other researchers. There is value not only in the discovery itself, but also in the road that leads to it.