A note on the mean value of the zeta and $L$-functions. XIV
A note on the mean value of the zeta and $L$-functions. XIV
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DOI：
10.3792/pjaa.80.28
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发表时间：
1999-10
期刊：
影响因子：
--
通讯作者：
Y. Motohashi
中科院分区：
文献类型：
--
作者：
Y. Motohashi
本文的目的是研究自同构l函数均值统一理论的可行性，这是该领域的一个迫切需要。这是从第十二部分（[14]）开始的调查的结果，其中在自同构表示理论的基础上奠定了框架，并设想了均值的一般方法。具体地说，这里表明，由A. Good[7]提出并经M. Jutila[9]大大改进的内积方法，应当加以完善，以便在自同构的概念内求得上半平面上任意尖形的l函数的均方。基里洛夫地图是我们的关键工具。由于其几何性质，我们的方法似乎可以推广到更大的线性李群。这张钞票基本上是独立的。
The aim of the present note is to develop a study on the feasibility of a unified theory of mean values of automorphic L-functions, a desideratum in the field. This is an outcome of the investigation commenced with the part XII ([14]), where a framework was laid on the basis of the theory of automorphic representations, and a general approach to the mean values was envisaged. Specifically, it is shown here that the inner-product method, which was initiated by A. Good [7] and greatly enhanced by M. Jutila [9], ought to be brought to perfection so that the mean square of the L-function attached to any cusp form on the upper half-plane could be reached within the notion of automorphy. The Kirillov map is our key implement. Because of its geometric nature, our method appears to extend to bigger linear Lie groups. This note is essentially self-contained.