TY - JOUR
T1 - Derivatives and exceptional poles of the local exterior square L-function for GLm
AU - Jo, Yeongseong
N1 - Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/4/1
Y1 - 2020/4/1
N2 - Let π be an irreducible admissible representation of GLm(F) , where F is a non-archimedean local field of characteristic zero. In 1990’s Jacquet and Shalika established an integral representation for the exterior square L-function. We complete, following the method developed by Cogdell and Piatetski-Shapiro, the computation of the local exterior square L-function L(s, π, ∧ 2) via the integral representation in terms of L-functions of supercuspidal representations by a purely local argument. With this result, we show the equality of the local analytic L-functions L(s, π, ∧ 2) via the integral representation for the irreducible admissible representation π for GLm(F) and the local arithmetic L-functions L(s, ∧ 2(ϕ(π))) of its Langlands parameter ϕ(π) through local Langlands correspondence.
AB - Let π be an irreducible admissible representation of GLm(F) , where F is a non-archimedean local field of characteristic zero. In 1990’s Jacquet and Shalika established an integral representation for the exterior square L-function. We complete, following the method developed by Cogdell and Piatetski-Shapiro, the computation of the local exterior square L-function L(s, π, ∧ 2) via the integral representation in terms of L-functions of supercuspidal representations by a purely local argument. With this result, we show the equality of the local analytic L-functions L(s, π, ∧ 2) via the integral representation for the irreducible admissible representation π for GLm(F) and the local arithmetic L-functions L(s, ∧ 2(ϕ(π))) of its Langlands parameter ϕ(π) through local Langlands correspondence.
KW - Bernstein–Zelevinsky derivatives
KW - Exceptional poles
KW - Jacquet–Shalika integral
KW - Local exterior square L-function
UR - http://www.scopus.com/inward/record.url?scp=85066033389&partnerID=8YFLogxK
U2 - 10.1007/s00209-019-02327-4
DO - 10.1007/s00209-019-02327-4
M3 - Article
AN - SCOPUS:85066033389
SN - 0025-5874
VL - 294
SP - 1687
EP - 1725
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 3-4
ER -