On the Hecke fields of Galois representations

Dohoon Choi, Yuichiro Taguchi

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)813-821
Number of pages9
JournalBulletin of the London Mathematical Society
Volume48
Issue number5
DOIs
Publication statusPublished - 2016 Oct 1
Externally publishedYes

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Galois Representations
Eigenvalue
Automorphic Representations
Rationality
Prime number

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 journalArticle

Choi, Dohoon ; Taguchi, Yuichiro. / On the Hecke fields of Galois representations. In: Bulletin of the London Mathematical Society. 2016 ; Vol. 48, No. 5. pp. 813-821.
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