Gauss sums on GL2(Z/plZ)

[摘要] We determine explicitly the Gauss sum tau(l)(chi, e) = Sigma(X is an element of GL2(Z/plZ)) chi(X)e(TrX) on the general linear group GL(2)(Z/p(l)Z) for every irreducible character chi of GL(2)(Z/p(l)L) and a nontrivial additive character e of Z/p(l)Z, where p is an odd prime and I is an integer >= 2. While there are several studies of the Gauss sums on finite algebraic groups defined over a finite field; this paper seems to be the first one which determines the Gauss sums on a matrix group over a finite ring. (C) 2013 Elsevier Inc. All rights reserved.

[发布日期] 2013-12-15

[关键词] General linear group;Irreducible character;Gauss sum