Archimedean zeta integrals on $GL_n \times GL_m$ and $SO_{2n+1} \times GL_m$

Details Archimedean zeta integrals on $GL_n \times GL_m$ and $SO_{2n+1} \times GL_m$ Archimedean zeta integrals on $GL_n \times GL_m$ and $SO_{2n+1} \times GL_m$

2011-02-11

arxiv.org/abs/1102.2457v1

Mathematics

Number Theory

Scientific paper

In this paper, we evaluate archimedean zeta integrals for automorphic $L$-functions on $GL_n \times GL_{n-1+\ell}$ and on $ SO_{2n+1} \times GL_{n+\ell}$, for $\ell=-1$, $0$, and $1$. In each of these cases, the zeta integrals in question may be expressed as Mellin transforms of products of class one Whittaker functions. Here, we obtain explicit expressions for these Mellin transforms in terms of Gamma functions and Barnes integrals.

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