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Relations between values at \(T\)-tuples of negative integers of twisted multivariable zeta series associated to polynomials of several variables. (English) Zbl 1198.11076

Summary: We give a new and very concise proof of the existence of a holomorphic continuation for a large class of twisted multivariable zeta functions. To do this, we use a simple method of “decalage” that avoids using an integral representation of the zeta function. This allows us to derive explicit recurrence relations between the values at \(T\)-tuples of negative integers. This also extends some earlier results of several authors where the underlying polynomials were products of linear forms.

MSC:

11M32 Multiple Dirichlet series and zeta functions and multizeta values
11M41 Other Dirichlet series and zeta functions
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