Equidistribution, L-functions and ergodic theory: on some problems of Yu. Linnik
Equidistribution, L-functions and ergodic theory: on some problems of Yu. Linnik
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DOI：
10.4171/022-2/19
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
P. Michel;Akshay Venkatesh
中科院分区：
文献类型：
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作者：
P. Michel;Akshay Venkatesh
Linnik的一个老问题是关于大球面上积分点的均匀分布。这个问题被证明是非常丰富的：它与模形式、L函数的次凸估计以及齐次空间上的环面作用的动力学密切相关。事实上，Linnik使用遍历方法给出了部分答案，而Duke使用调和分析和模形式完全回答了他的问题。我们回顾了这些想法的背景及其在过去几十年的发展。
An old question of Linnik asks about the equidistribution of integral points on a large sphere. This question proved to be very rich: it is intimately linked to modular forms, to subconvex estimates for L-functions, and to dynamics of torus actions on homogeneous spaces. Indeed, Linnik gave a partial answer using ergodic methods, and his question was completely answered by Duke using harmonic analysis and modular forms. We survey the context of these ideas and their developments over the last decades.