It is well known by the strong multiplicity one thatπis uniquely determined by the Satake parameter c(π,v)for almost all v.Also,it suffices for us to test only finitely many v.We proved some S-effective version of m...It is well known by the strong multiplicity one thatπis uniquely determined by the Satake parameter c(π,v)for almost all v.Also,it suffices for us to test only finitely many v.We proved some S-effective version of multiplicity one theorems.Roughly speaking,ifπandπ′are not equivalent,then there is also a bound N(S)which is some expression in terms of K,d and max(N(π),N(π′)),which are analytic conductor ofπandπ′,respectively(will be defined soon),such that there is a v/∈S withπv～=π′vand N pv<N.We also proved S-effective multiplicity one for the Chebotarev Density Theorem,and for GL(1).展开更多
基金supported by the State Key Development Program for Basic Researchof China(973 project)(Grant No.2013CB834202)National Natural Science Foundation of China(Grant No.11321101)the One Hundred Talent’s Program from Chinese Academy of Science
文摘It is well known by the strong multiplicity one thatπis uniquely determined by the Satake parameter c(π,v)for almost all v.Also,it suffices for us to test only finitely many v.We proved some S-effective version of multiplicity one theorems.Roughly speaking,ifπandπ′are not equivalent,then there is also a bound N(S)which is some expression in terms of K,d and max(N(π),N(π′)),which are analytic conductor ofπandπ′,respectively(will be defined soon),such that there is a v/∈S withπv～=π′vand N pv<N.We also proved S-effective multiplicity one for the Chebotarev Density Theorem,and for GL(1).
