当前位置: X-MOL 学术Commun. Number Theory Phys. › 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.)
Differential equations in automorphic forms
Communications in Number Theory and Physics ( IF 1.2 ) Pub Date : 2018-01-01 , DOI: 10.4310/cntp.2018.v12.n4.a4
Kim Klinger-Logan 1
Affiliation  

Physicists such as Green, Vanhove, et al show that differential equations involving automorphic forms govern the behavior of gravitons. One particular point of interest is solutions to $(\Delta-\lambda)u=E_{\alpha} E_{\beta}$ on an arithmetic quotient of the exceptional group $E_8$. We use spectral theory solve $(\Delta-\lambda)u=E_{\alpha}E_{\beta}$ on the simpler space $SL_2(\mathbb{Z})\backslash SL_2(\mathbb{R})$. The construction of such a solution uses Arthur truncation, the Maass-Selberg formula, and automorphic Sobolev spaces.

中文翻译:

自守形式的微分方程

Green、Vanhove 等物理学家表明,涉及自守形式的微分方程控制着引力子的行为。一个特别的兴趣点是 $(\Delta-\lambda)u=E_{\alpha} E_{\beta}$ 在异常群 $E_8$ 的算术商上的解。我们使用谱理论在更简单的空间 $SL_2(\mathbb{Z})\backslash SL_2(\mathbb{R})$ 上求解 $(\Delta-\lambda)u=E_{\alpha}E_{\beta}$ . 此类解决方案的构造使用 Arthur 截断、Maass-Selberg 公式和自守 Sobolev 空间。
更新日期:2018-01-01
down
wechat
bug