Archimedean zeta integrals for $GL(3)\times GL(2)$

Miki Hirano; Taku Ishii; Tadashi Miyazaki

Archimedean zeta integrals for $GL(3)\times GL(2)$

Number Theory 2021-04-13 v1 Representation Theory

Authors: Miki Hirano , Taku Ishii , Tadashi Miyazaki

Abstract

In this article, we give explicit formulas of archimedean Whittaker functions on $GL(3)$ and $GL(2)$ . Moreover, we apply those to the calculation of archimedean zeta integrals for $GL(3)\times GL(2)$ , and show that the zeta integral for appropriate Whittaker functions is equal to the associated $L$ -factors.

Keywords

zeta functions

Cite

@article{arxiv.2104.05042,
  title  = {Archimedean zeta integrals for $GL(3)\times GL(2)$},
  author = {Miki Hirano and Taku Ishii and Tadashi Miyazaki},
  journal= {arXiv preprint arXiv:2104.05042},
  year   = {2021}
}

Comments

Final version with minor modifications, to appear in Memoirs of the American Mathematical Society. 126 pages

Archimedean zeta integrals for $GL(3)\times GL(2)$

Abstract

Keywords

Cite

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