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Bulletin of the London Mathematical Society Advance Access published online on May 22, 2009
Bulletin of the London Mathematical Society, doi:10.1112/blms/bdp043
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© 2009 London Mathematical Society

Zeros and the universality for the Euler–Zagier–Hurwitz type of multiple zeta-functions

Takashi Nakamura

Department of Mathematics Faculty of Science and Technology
Tokyo University of Science
Noda
CHIBA 278-8510
Japan

Received 7 March 2008. Revision received 28 October 2008.

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.

The author is supported by JSPS Research Fellowship for Young Scientists (JSPS Research Fellow PD).

2000 Mathematics Subject Classification 11M06 (primary), 11M26 (secondary).


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