Talk on Siegel theta series and modular forms

overview

• Siegel theta series
• Siegel modular forms
• Siegel-Weil formula

basic mathematics

• 두 $n\times n$행렬 $A=(a_{ij})$와 $B=(b_{ij})$에 대하여, $AB$의 대각합은 다음과 같이 주어진다

$$ \operatorname{tr}(AB)=\sum_{i,j=1}^{n}a_{ij}b_{ji} $$

• $n=2$인 경우 $\operatorname{tr}(AB)=a_{1,1} b_{1,1}+a_{2,1} b_{1,2}+a_{1,2} b_{2,1}+a_{2,2} b_{2,2}$
• $n=3$인 경우 $\operatorname{tr}(AB)=a_{1,1} b_{1,1}+a_{2,1} b_{1,2}+a_{3,1} b_{1,3}+a_{1,2} b_{2,1}+a_{2,2} b_{2,2}+a_{3,2} b_{2,3}+a_{1,3} b_{3,1}+a_{2,3} b_{3,2}+a_{3,3} b_{3,3}$

related items

• Siegel-Weil formula