INVESTIGADORES
DICKENSTEIN Alicia Marcela
artículos
Título:
Bases in the solution space of the Mellin system
Autor/es:
A. DICKENSTEIN, T. SADYKOV
Revista:
SBORNIK MATHEMATICS
Editorial:
Turpion-Moscow LTD
Referencias:
Lugar: Moscu; Año: 2007 vol. 189 p. 1277 - 1298
ISSN:
1064-5616
Resumen:
Local holomorphic solutions z=z(a) to a univariate sparse polynomial equation p(z) =0, in terms of its vector of complex coefficients a, are classically known to satisfy holonomic systems of linear partial differential equations with polynomial coefficients. In this paper we investigate one of such systems of differential equations which was introduced by Mellin. We compute the holonomic rank of the Mellin system as well as the dimension of the space of its algebraic solutions. Moreover, we construct explicit bases of solutions in terms of the roots of p and their logarithms. We show that the monodromy of the Mellin system is always reducible and give some factorization results in the univariate case.