纺织高校基础科学学报2017，Vol.30Issue(3)：293-301,9.DOI:10.13338/j.issn.1006-8341.2017.03.001
关于Kuznetsov求和公式的注记
Note on the Kuznetsov sum formula
KANEMITSU S 1AGARWAL P 2李海龙3
作者信息
- 1. 日本近畿大学信息科学学院,日本福冈820-8555
- 2. 阿南德工程国际学院数学学院,印度拉贾斯坦邦斋浦尔303012
- 3. 渭南师范学院数学学院,陕西渭南714000
- 折叠
摘要
Abstract
In the theory of automorphic L-functions,the Kuznetsov trace formula is one of the highlights.There are a few different statements of the formula.The most comprehensive one for a Fuchsian group of the first kind is given in Iwaniec's book.In Motohashi's book,the case of the full modular group is treated and their results look different.In the companion paper by Ma and Agarwal,it is shown on the basis of modular relation principle that the statement of Motohashi is another version of Theorem 2.4 and that it has different outlook lacking the Neumann series.We slightly generalized the method of Selberg adopted by Motohashi of equating the two different expressions for the inner product of two Poincaré series to deduce Theorem 2.4 below,which is the reversed form according to Iwaniec but it is the form stated as the Kuznetsov trace formula in most of the literature.In this note we shall elaborate the proof in the Ma and Agarwal's paper using more familiar special functions and give proofs of intermediate formulas involving Bessel functions.This makes the situation more transparent surrouding the Kuznetsov trace formula and make it more accessible.关键词
Kuznetsov和/自守L-函数/Neumann级数/Poincaré级数/Bessel函数Key words
Kuznetsov sum/automorphic L-function/Neumann series/Poincaré series/Bessel function分类
数理科学引用本文复制引用
KANEMITSU S,AGARWAL P,李海龙..关于Kuznetsov求和公式的注记[J].纺织高校基础科学学报,2017,30(3):293-301,9.
