Abstract
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
| Original language | English |
|---|---|
| Pages (from-to) | 1995-2010 |
| Number of pages | 16 |
| Journal | International Journal of Number Theory |
| Volume | 9 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - Dec 2013 |
| Externally published | Yes |
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Keywords
- exterior square L-function
- Local newform
- Rankin-Selberg method
- zeta integral
ASJC Scopus subject areas
- Algebra and Number Theory
Cite this
Local newforms and formal exterior square l-functions. / Miyauchi, Michitaka; Yamauchi, Takuya.
In: International Journal of Number Theory, Vol. 9, No. 8, 12.2013, p. 1995-2010.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Local newforms and formal exterior square l-functions
AU - Miyauchi, Michitaka
AU - Yamauchi, Takuya
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 - exterior square L-function
KW - Local newform
KW - Rankin-Selberg method
KW - zeta integral
UR - http://www.scopus.com/inward/record.url?scp=84889671379&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84889671379&partnerID=8YFLogxK
U2 - 10.1142/S179304211350070X
DO - 10.1142/S179304211350070X
M3 - Article
VL - 9
SP - 1995
EP - 2010
JO - International Journal of Number Theory
JF - International Journal of Number Theory
SN - 1793-0421
IS - 8
ER -