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We derive some new signed Mahonian polynomials over the complex reflectiongroup $G(r,1,n)=C_r\wr\mathfrak{S}_n$, where the "sign" is taken to be any ofthe $2r$ $1$-dim characters and the "Mahonian" statistics are the$\mathsf{lmaj}$ defined by Bagno and the $\mathsf{sor}$ defined by Eu et al.Various new signed Mahonian polynomials over Coxeter groups of types $B_n$ and$D_n$ are derived as well. We also investigate the signed counting polynomialson $G(r,1,n)$ for those statistics with the distribution $[r]_q[2r]_q\cdots[nr]_q$.

Signed Mahonian polynomials for major and sorting indices