ABSTRACT Description of convergence domains for multiple power series is a quite difficult problem. In 1889 J.Horn showed that the case of hypergeomteric series is more favourable. He found a parameterization formula for surfaces of conjugative radii of such series. But until recently almost nothing was known about the description of convergence domains in terms of functional inequalities relatively moduli of series variables. In this paper we give a such description for hypergeometric series representing solutions to tetranomial algebraic equations. In our study we use the remarkable observation by M. Kapranov (1991) consisting in the fact that the Horn's formulae give a parameterization of discriminant locus for a corresponding A-discriminant. We prove that usually the considered convergence domains are determined by a signle or two inequalities , where ρ is a reduced discriminant.

中文翻译：

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代数函数的二维超几何级数的收敛

摘要 多重幂级数收敛域的描述是一个相当困难的问题。1889 年 J.Horn 表明超几何级数的情况更有利。他找到了此类系列共轭半径曲面的参数化公式。但直到最近，关于收敛域的描述几乎一无所知，根据函数不等式相对于序列变量的模数。在本文中，我们对表示四项式代数方程解的超几何级数给出了这样的描述。在我们的研究中，我们使用了 M. Kapranov (1991) 的非凡观察，包括 Horn 公式给出了相应 A 判别式的判别轨迹的参数化。