Stable local trace formula  

作　　者：PENG ZhiFeng 

机构地区：[1]Department of Mathematics, Nanjing University

出　　处：《Science China Mathematics》2014年第12期2509-2518,共10页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11471154)

摘　　要：Langlands program is the central concern of modern number theory. In general, we think that the main tool for studying this program is the trace formula. Arthur-Selberg's trace formula is successful in solving the endoscopic case of Langlands program. Arthur stabilized the geometric side of the local trace formula in the general case, but did not stabilize the general spectral. This paper aims to solve the general case by different method in the Archimedean case, by directly stabilizing the spectral side of the local trace formula, and obtains the stable local trace formula.Langlands program is the central concern of modern number theory. In general, we think that the main tool for studying this program is the trace formula. Arthur-Selberg＇s trace formula is successful in solving the endoscopic case of Langlands program. Arthur stabilized the geometric side of the local trace formula in the general case, but did not stabilize the general spectral. This paper aims to solve the general case by different method in the Archimedean case, by directly stabilizing the spectral side of the local trace formula, and obtains the stable local trace formula.

关 键 词：Langlands program trace formula Arthur-Selberg＇s trace formula 

分 类 号：O156[理学—数学]