• Corpus ID: 118865544

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

@article{Ishii2011ArchimedeanZI,
  title={Archimedean zeta integrals on \$GL\_n \times GL\_m\$ and \$SO\_\{2n+1\} \times GL\_m\$},
  author={Taku Ishii and Eric Stade},
  journal={arXiv: Number Theory},
  year={2011}
}
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. 
1 Citations
A Classical Limit of Noumi's q-Integral Operator
We demonstrate how a known Whittaker function integral identity arises from the t = 0 and q! 1 limit of the Macdonald polynomial eigenrelation satisfied by Noumi's q-integral operator.

References

SHOWING 1-10 OF 29 REFERENCES
Rankin-Selberg convolutions for SO[2l+1] × GL[n] : local theory
Introduction and preliminaries The integrals to be studied Estimates for Whittaker functions on $G_\ell$ (nonarchimedean case) Estimates for Whittaker functions on $G_\ell$ (archimedean case)
ArchimedeanL-factors onGL(n) ×GL(n) and generalized Barnes integrals
The Rankin-Selberg method associates, to each local factorL(s, πv × πv′) of an automorphicL-function onGL(n) ×GL(n), a certain local integral of Whittaker functions for πv andv′. In this paper we
New formulas for Whittaker functions on GL(n,R)
Mellin transforms of GL(n, R) whittaker functions
Using a known recursive formula for the class one principal series GL(n, R) Whittaker function, we deduce a recursive formula for the multiple Mellin transform of this function. From the latter
The Rankin–Selberg Method: A Survey
The Multiplicity One Theorem for GL n
The purpose of this paper is to establish preliminary results in the theory of representations in the direction of a systematic treatment of Hecke-theory for the group GLn. In particular, special
Spinor L-functions for generic cusp forms on GSp(2) belonging to principal series representations
Let G = GSp(2) be the symplectic group with similitude of degree two, which is defined over Q. For a generic cusp form F on the adelized group G A whose archimedean type is a principal series
Whittaker Functions on Real Semisimple Lie Groups of Rank Two
  • Taku Ishii
  • Mathematics
    Canadian Journal of Mathematics
  • 2010
Abstract We give explicit formulas for Whittaker functions on real semisimple Lie groups of real rank two belonging to the class one principal series representations. By using these formulas we
A Course of Modern Analysis
TLDR
The volume now gives a somewhat exhaustive account of the various ramifications of the subject, which are set out in an attractive manner and should become indispensable, not only as a textbook for advanced students, but as a work of reference to those whose aim is to extend the knowledge of analysis.
Representation Theory: A First Course
This volume represents a series of lectures which aims to introduce the beginner to the finite dimensional representations of Lie groups and Lie algebras. Following an introduction to representation
...
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