Test vectors for Rankin-Selberg $L$-functions

Andrew R. Booker; M. Krishnamurthy; Min Lee

Test vectors for Rankin-Selberg $L$-functions

Number Theory 2019-03-11 v1 Representation Theory

Authors: Andrew R. Booker , M. Krishnamurthy , Min Lee

Abstract

We study the local zeta integrals attached to a pair of generic representations $(\pi,\tau)$ of $GL_n\times GL_m$ , $n>m$ , over a $p$ -adic field. Through a process of unipotent averaging we produce a pair of corresponding Whittaker functions whose zeta integral is non-zero, and we express this integral in terms of the Langlands parameters of $\pi$ and $\tau$ . In many cases, these Whittaker functions also serve as a test vector for the associated Rankin-Selberg (local) $L$ -function.

Keywords

zeta functions langlands correspondence

Cite

@article{arxiv.1903.03458,
  title  = {Test vectors for Rankin-Selberg $L$-functions},
  author = {Andrew R. Booker and M. Krishnamurthy and Min Lee},
  journal= {arXiv preprint arXiv:1903.03458},
  year   = {2019}
}

Comments

arXiv admin note: text overlap with arXiv:1804.07721

Test vectors for Rankin-Selberg $L$-functions

Abstract

Keywords

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