Аннотация:

Systems of non-algebraic equations may have infinite number of common zeroes, therefore their power sums are usually considered with negative exponents. Under certain conditions on a system the series obtained can be computed as integrals over local cycles. Such integrals are called pseudopower or $\sigma$-power sums. Similar to algebraic case, there are recurrent relations between them, which are analogues of the classical Newton identities.

Analogues of the Newton identities are necessary for generalization of the L.A. Aizenberg elimination method based on the multidimensional logarithmic residue formula.

In some cases $\sigma$-power sums and relations between them are known. In this paper we consider systems of functions holomorphic in a neighborhood of the origin such that lower homogeneous terms of their Taylor expansions at the origin admit common monomial factors. For such systems we compute $\sigma$-power sums and establish recurrent relations between them.