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International Mathematics Research Notices Advance Access originally published online on January 2, 2009
International Mathematics Research Notices (2009) 2009:241-290, doi:10.1093/imrn/rnn131 published on January 23, 2009
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© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Zeta Functions for G2 and Their Zeros

Masatoshi Suzuki1 and Lin Weng2,3

1 Graduate School of Mathematics, The University of Tokyo, Komba 3-8-1, Meguro-ku, Tokyo 153-8914, Japan
2 Graduate School of Mathematics, Kyushu University, 6-10-1, Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan
3 Chennai Mathematical Institute, Plot H1, SIPCOT IT Park, Padur PO, Siruseri 603103, India

Correspondence: Correspondence to be sent to: weng{at}math.kyushu-u.ac.jp

The exceptional group G2 has two maximal parabolic subgroups Formula corresponding to the so-called long root and short root. In this paper, the second named author introduces two zeta functions associated with Formula and Formula respectively, and the first named author proves that these zetas satisfy the Riemann hypothesis.


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