Zeta Functions for G2 and Their Zeros

The exceptional group G2 has two maximal parabolic subgroups $P_{\mathrm{long}},P_{\mathrm{short}}$ corresponding to the so-called long root and short root. In this paper, the second named author introduces two zeta functions associated with $(G_{2},P_{\mathrm{long}})$ and $(G_{2},P_{\mathrm{short}})$ respectively, and the first named author proves that these zetas satisfy the Riemann hypothesis.