TY - JOUR
T1 - Local newforms and formal exterior square l-functions
AU - Miyauchi, Michitaka
AU - Yamauchi, Takuya
N1 - Funding Information:
The first author expresses his appreciation to Taku Ishii for giving an introductory talk on this subject at Tambara Institute of Mathematical Sciences, The University of Tokyo, and to Takayuki Oda for inviting him to that conference. The authors would like to thank Tomonori Moriyama for helpful conversations and Yoshi-hiro Ishikawa for his useful comments. The first author is partially supported by JSPS Grant-in-Aid for Scientific Research No. 21540017. The second author is partially supported by JSPS Grant-in-Aid for Scientific Research No. 23740027 and JSPS Postdoctoral Fellowships for Research Abroad No. 378. The authors would like to thank the referee for a careful reading of the manuscript and useful suggestions on the presentation of this paper.
PY - 2013/12
Y1 - 2013/12
N2 - Let F be a non-archimedean local field of characteristic zero. Jacquet and Shalika attached a family of zeta integrals to unitary irreducible generic representations π of GLn(F). In this paper, we show that the Jacquet-Shalika integral attains a certain L-function, the so-called formal exterior square L-function, when the Whittaker function is associated to a newform for π. By considerations on the Galois side, formal exterior square L-functions are equal to exterior square L-functions for some principal series representations. Local newform, exterior square L-function, Rankin-Selberg method, zeta integral 22E50, 22E35
AB - Let F be a non-archimedean local field of characteristic zero. Jacquet and Shalika attached a family of zeta integrals to unitary irreducible generic representations π of GLn(F). In this paper, we show that the Jacquet-Shalika integral attains a certain L-function, the so-called formal exterior square L-function, when the Whittaker function is associated to a newform for π. By considerations on the Galois side, formal exterior square L-functions are equal to exterior square L-functions for some principal series representations. Local newform, exterior square L-function, Rankin-Selberg method, zeta integral 22E50, 22E35
KW - Local newform
KW - Rankin-Selberg method
KW - exterior square L-function
KW - zeta integral
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U2 - 10.1142/S179304211350070X
DO - 10.1142/S179304211350070X
M3 - Article
AN - SCOPUS:84889671379
VL - 9
SP - 1995
EP - 2010
JO - International Journal of Number Theory
JF - International Journal of Number Theory
SN - 1793-0421
IS - 8
ER -