Abstract
It is known that, in many cases, the field (known as the Hecke field) generated by all Hecke eigenvalues of an elliptic modular newform f is in fact generated by the pth Hecke eigenvalue ap of f for a single prime number p. In this paper, we study the density of such primes in a more general situation in terms of Galois representations. This is applied to the study of the fields of rationality of certain automorphic representations.
| Original language | English |
|---|---|
| Pages (from-to) | 813-821 |
| Number of pages | 9 |
| Journal | Bulletin of the London Mathematical Society |
| Volume | 48 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 2016 Oct 1 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Mathematics(all)
Cite this
On the Hecke fields of Galois representations. / Choi, Dohoon; Taguchi, Yuichiro.
In: Bulletin of the London Mathematical Society, Vol. 48, No. 5, 01.10.2016, p. 813-821.Research output: Contribution to journal › Article
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TY - JOUR
T1 - On the Hecke fields of Galois representations
AU - Choi, Dohoon
AU - Taguchi, Yuichiro
PY - 2016/10/1
Y1 - 2016/10/1
N2 - It is known that, in many cases, the field (known as the Hecke field) generated by all Hecke eigenvalues of an elliptic modular newform f is in fact generated by the pth Hecke eigenvalue ap of f for a single prime number p. In this paper, we study the density of such primes in a more general situation in terms of Galois representations. This is applied to the study of the fields of rationality of certain automorphic representations.
AB - It is known that, in many cases, the field (known as the Hecke field) generated by all Hecke eigenvalues of an elliptic modular newform f is in fact generated by the pth Hecke eigenvalue ap of f for a single prime number p. In this paper, we study the density of such primes in a more general situation in terms of Galois representations. This is applied to the study of the fields of rationality of certain automorphic representations.
UR - http://www.scopus.com/inward/record.url?scp=84995777303&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84995777303&partnerID=8YFLogxK
U2 - 10.1112/blms/bdw042
DO - 10.1112/blms/bdw042
M3 - Article
AN - SCOPUS:84995777303
VL - 48
SP - 813
EP - 821
JO - Bulletin of the London Mathematical Society
JF - Bulletin of the London Mathematical Society
SN - 0024-6093
IS - 5
ER -