Complete settling of the multiplier conjecture for the case of n=3p^r  

作　　者：丘维声 

出　　处：《Science China Mathematics》2002年第9期1117-1134,共18页中国科学：数学（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China (Grant No. 19831070).

摘　　要：In this paper we improve the character approach to the multiplier conjecture that we presented after 1992, and thus we have made considerable progress in the case of n = 3n1. We prove that in the case of n = 3n1 Second multiplier theorem remains true if the assumption “n1 > λ” is replaced by “(n1, λ) = 1”. Consequentially we prove that if we let D be a (v, k, λ)-difference set in an abelian group G, and n = 3pr for some prime p, (p,v) = 1, then p is a numerical multiplier of D.In this paper we improve the character approach to the multiplier conjecture that we presented after 1992, and thus we have made considerable progress in the case of n=3n1. We prove that in the case of n = 3n1 Second multiplier theorem remains true if the assumption 'n1 ＞λ' is replaced by '(n1, λ)=1'.Consequentially we prove that if we let D be a (v, κ,λ)-difference set in an abelian group G, and n=3pr for some prime p, (p,v)=1, then p is a numerical multiplier of D.

关 键 词：difference set  MULTIPLIER conjecture  group ring  character  INVERSION formula  cyclo-tomic field  CH-equations  basic equation. 

分 类 号：O152[理学—数学]