Dualities for absolute zeta functions and multiple gamma functions
Copyright policy )Dualities for absolute zeta functions and multiple gamma functions
We study absolute zeta functions from the view point of a canonical normalization. We introduce the absolute Hurwitz zeta function for the normalization. In particular, we show that the theory of multiple gamma and sine functions gives good normalizations in cases related to the Kurokawa tensor product. In these cases, the functional equation of the absolute zeta function turns out to be equivalent to the simplicity of the associated non-classical multiple sine function of negative degree.
Mathematics - Number Theory, Hurwitz and Lerch zeta functions, absolute zeta function, 11M06, Absolute zeta function, multiple gamma function, \(\zeta (s)\) and \(L(s, \chi)\), Multiple Dirichlet series and zeta functions and multizeta values, FOS: Mathematics, absolute Hurwitz zeta function, Kurokawa tensor product, Number Theory (math.NT), multiple sine function
Mathematics - Number Theory, Hurwitz and Lerch zeta functions, absolute zeta function, 11M06, Absolute zeta function, multiple gamma function, \(\zeta (s)\) and \(L(s, \chi)\), Multiple Dirichlet series and zeta functions and multizeta values, FOS: Mathematics, absolute Hurwitz zeta function, Kurokawa tensor product, Number Theory (math.NT), multiple sine function
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