클링겐-지겔 (Klingen-Siegel) 정리

개요

• F : totally real 수체
• \([F: \mathbb{Q}]=n\)
• \(m>0\)일 때, 다음을 만족하는 적당한 유리수 \(r(m)\in \mathbb{Q}\)가 존재한다

\[\zeta_{F}(2m)=r(m)\frac{\pi^{2mn}}{\sqrt{|d_{F}|}}\]

수학용어번역

• Klingen - 발음사전 Forvo
• Siegel - 발음사전 Forvo

관련논문

• Beilinson, Alexander, Guido Kings, and Andrey Levin. ‘Topological Polylogarithms and \(p\)-Adic Interpolation of \(L\)-Values of Totally Real Fields’. arXiv:1410.4741 [math], 17 October 2014. http://arxiv.org/abs/1410.4741.
• Nori, Madhav V. "Some Eisenstein cohomology classes for the integral unimodular group." Proceedings of the International Congress of Mathematicians. Vol. 1. 1995. http://www.mathunion.org/ICM/ICM1994.1/Main/icm1994.1.0690.0696.ocr.pdf
• Sczech, Robert. ‘Eisenstein Group Cocycles for GL N and Values ofL-Functions’. Inventiones Mathematicae 113, no. 1 (1 December 1993): 581–616. doi:10.1007/BF01244319.

사전 형태의 자료

• http://planetmath.org/SiegelKlingenTheorem.html