PGL2 (Fℓ) number fields with rational companion forms

David P. Roberts

doi:10.1142/S1793042118500501

PGL₂ (Fℓ) number fields with rational companion forms

David P. Roberts

Mathematics (Morris)

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

1 Scopus citations

Abstract

We give a list of PGL2(Fℓ) number fields for ℓ ≥ 11 which have rational companion forms. Our list has 53 fields and seems likely to be complete. Some of the fields on our list are very lightly ramified for their Galois group.

Original language	English (US)
Pages (from-to)	825-845
Number of pages	21
Journal	International Journal of Number Theory
Volume	14
Issue number	3
DOIs	https://doi.org/10.1142/S1793042118500501
State	Published - Apr 1 2018

Bibliographical note

Publisher Copyright:
© 2018 World Scientific Publishing Company.

Keywords

Galois group
Number field
companion form
discriminant
modular form

Publisher link

10.1142/S1793042118500501

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Cite this

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abstract = "We give a list of PGL2(Fℓ) number fields for ℓ ≥ 11 which have rational companion forms. Our list has 53 fields and seems likely to be complete. Some of the fields on our list are very lightly ramified for their Galois group.",

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KW - Galois group

KW - Number field

KW - companion form

KW - discriminant

KW - modular form

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