Stability of Asai local factors for $GL(2)$
Number Theory
2019-08-13 v2 Representation Theory
Abstract
Let be a non-archimedean local field of characteristic not equal to and let be a quadratic algebra. We prove the stability of local factors attached to (complex) irreducible admissible representations of via the Rankin-Selberg method under highly ramified twists. This includes both the Asai as well as the Rankin-Selberg local factors attached to pairs. Our method relies on expressing the gamma factor as a Mellin transform using Bessel functions.
Keywords
Cite
@article{arxiv.1906.06585,
title = {Stability of Asai local factors for $GL(2)$},
author = {Yeongseong Jo and Muthu Krishnamurthy},
journal= {arXiv preprint arXiv:1906.06585},
year = {2019}
}
Comments
Our result is extended to the split case