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Zeros and the universality for the Euler–Zagier–Hurwitz type of multiple zeta‐functions
Author(s) -
Nakamura Takashi
Publication year - 2009
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdp043
Subject(s) - mathematics , universality (dynamical systems) , euler's formula , hurwitz matrix , riemann zeta function , pure mathematics , type (biology) , hurwitz polynomial , routh–hurwitz stability criterion , mathematical analysis , physics , parametric statistics , ecology , statistics , quantum mechanics , biology , polynomial
In this paper, we show relations between the zero‐free region and the universality for the Euler–Zagier–Hurwitz type of multiple zeta‐functions. Roughly speaking these relations imply that we can obtain the universality for the Euler–Zagier–Hurwitz type of multiple zeta‐functions by their zero‐free property, and vice versa. Moreover, we obtain the non‐trivial zeros, joint denseness and functional independence for the Euler–Zagier–Hurwitz type of multiple zeta‐functions.