The problem of the correct computation of the vacuum energy contribution to cosmological constant is discussed in the context of the relativistic invariant zeta-function approach. This method is shown to yield the value of this quantity proportional to the fourth power of the (small) quantized field mass, while the dependence on the large mass scale is only logarithmic. This value is compared to the result obtained in the dimensional regularization scheme which also satisfies the relativistic invariance condition, and found to be the same up to irrelevant finite terms. The consequences of the renormalization group invariance are also briefly discussed.

PACS numbers: 11.10.-z, 11.10.Gh