Open AccessOn epsilon factors attached to supercuspidal representations of unramified 𝑈(2,1)
Author(s) -
Michitaka Miyauchi
Publication year - 2013
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/s0002-9947-2013-05859-x
Subject(s) - annotation , algorithm , computer science , type (biology) , artificial intelligence , semantics (computer science) , mathematics , biology , programming language , ecology
Let G G be the unramified unitary group in three variables defined over a p p -adic field F F with p ≠ 2 p \neq 2 . Gelbart, Piatetski-Shapiro and Baruch attached zeta integrals of Rankin-Selberg type to irreducible generic representations of G G . In this paper, we formulate a conjecture on L L - and ε \varepsilon -factors defined through zeta integrals in terms of newforms for G G , which is an analogue of the result by Casselman and Deligne for G L ( 2 ) \mathrm {GL}(2) . We prove our conjecture for the generic supercuspidal representations of G G .