Cosmological Constant and Zeta-Function

The relativistically invariant generalisation of the zeta-function method of evaluation of the vacuum energy contribution to the cosmological constant is discussed. It is shown that this value is determined by the fourth power of the quantised field mass, while the dependence from the large mass scale is only logarithmic. This value is compared to the result obtained in the dimensional regularization schemes which also satisfy 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