On the Hecke fields of Galois representations

Dohoon Choi; Yuichiro Taguchi

doi:10.1112/blms/bdw042

On the Hecke fields of Galois representations

Dohoon Choi, Yuichiro Taguchi

Research output: Contribution to journal › Article › peer-review

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 a_p 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	https://doi.org/10.1112/blms/bdw042
Publication status	Published - 2016 Oct 1
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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10.1112/blms/bdw042

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author = "Dohoon Choi and Yuichiro Taguchi",

note = "Funding Information: The first author was partially supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (ASARC, NRF-2007-0056093). The second author was partially supported by JSPS KAKENHI 25400016. Publisher Copyright: {\textcopyright} 2016 London Mathematical Society.",

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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.

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JO - Bulletin of the London Mathematical Society

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On the Hecke fields of Galois representations

Abstract

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