On a conjecture of Varchenko

摘要

This note was motivated by a problem posed by Varchenko in [7], (See also the earlier paper by Aomoto [2]), Let f,(x\ xB) (/ = 1,...,AT ~ I) be linear functions of n complex, variables, and let D, = {// = 0} C C" e the hyper-plancs defined as their corresponding zero loci. The product 0/ = JI/=i- f}'* I. where the A/ are complex parameters, is a multivalued holomorphic function " oft the complement.