Analytic Continuation for Solutions to the System of Trinomial Algebraic Equations

Abstract

In the paper, we deal with the problem of getting analytic continuations for the monomial function associated with a solution to the reduced trinomial algebraic system. In particular, we develop the idea of applying the Mellin-Barnes integral representation of the monomial function for solving the extension problem and demonstrate how to achieve the same result following the fact that the solution to the universal trinomial system is polyhomogeneous. As a main result, we construct Puiseux expansions (centred at the origin) representing analytic continuations of the monomial function.

Hypergeometric Series and the Mellin-Barnes Integrals for Zeros of a System of Laurent Polynomials

“…where each column vector Note that in [9] and [10] analogous results have been obtained for systems with a diagonal matrix ω and non-negative exponents of monomials λ ∈ Λ (j) . Applications of these results for study of discriminants of systems are given in [11].…”