On solutions of codimension-one $A$-hypergeometric systems

By a codimension-one system we mean a system whose lattice of relations has rank one. We consider codimension-one $A$-hypergeometric systems and explicitly construct some of the logarithmic series solutions at the origin. When the parameter vector $β$ is nonresonant we obtain a full set of logarithmic series solutions at the origin by this procedure. We also determine when a codimension-one system with nonresonant parameter can have maximal unipotent monodromy at the origin.

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