abstract: In papers by B. Klopsch, C. Voll and A. Stasinski, a new statistic L was defined, both on the symmetric and the hyperoctahedral group. We prove the conjectures appeared in the same papers about the generating function of this statistic, signed with the Coxeter length, over arbitrary quotients of Sn and Bn. We also define a natural analogue of L for Coxeter groups of type D and prove some results about its generating function. Finally we give other algebraic and geometric interpretations of L on type A and define new statistics in type B and D. This is joint work with Francesco Brenti.