当前位置: X-MOL 学术Nagoya Math. J. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
ANALYTIC PROPERTIES OF EISENSTEIN SERIES AND STANDARD -FUNCTIONS
Nagoya Mathematical Journal ( IF 0.8 ) Pub Date : 2020-07-21 , DOI: 10.1017/nmj.2020.11
OLIVER STEIN

We prove a functional equation for a vector valued real analytic Eisenstein series transforming with the Weil representation of $\operatorname{Sp}(n,\mathbb{Z})$ on $\mathbb{C}[(L^{\prime }/L)^{n}]$. By relating such an Eisenstein series with a real analytic Jacobi Eisenstein series of degree $n$, a functional equation for such an Eisenstein series is proved. Employing a doubling method for Jacobi forms of higher degree established by Arakawa, we transfer the aforementioned functional equation to a zeta function defined by the eigenvalues of a Jacobi eigenform. Finally, we obtain the analytic continuation and a functional equation of the standard $L$-function attached to a Jacobi eigenform, which was already proved by Murase, however in a different way.

中文翻译:

爱森斯坦级数和标准函数的解析性质

我们证明了向量值实解析 Eisenstein 级数转换的函数方程,其 Weil 表示为$\operatorname{Sp}(n,\mathbb{Z})$$\mathbb{C}[(L^{\prime }/L)^{n}]$. 通过将这样的 Eisenstein 级数与真实的解析 Jacobi Eisenstein 度数级数联系起来$n$,证明了这种 Eisenstein 级数的函数方程。采用由 Arakawa 建立的高阶 Jacobi 形式的加倍方法,我们将上述函数方程转换为由 Jacobi 特征型的特征值定义的 zeta 函数。最后,我们得到了标准的解析延拓和函数方程$L$- 附加到 Jacobi 特征形式的函数,这已经被 Murase 证明了,但是以不同的方式。
更新日期:2020-07-21
down
wechat
bug