Mathematical Research Letters

Volume 20 (2013)

Number 5

An application of Maeda’s conjecture to the inverse Galois problem

Pages: 985 – 993

DOI: http://dx.doi.org/10.4310/MRL.2013.v20.n5.a14

Author

Gabor Wiese (Faculté des Sciences, de la Technologie et de la Communication, Université du Luxembourg)

Abstract

It is shown that Maeda’s conjecture on eigenforms of level $1$ implies that for every positive even $d$ and every $p$ in a density-one set of primes, the simple group $\mathrm{PSL}_2(\mathbb{F}_{p^d})$ occurs as the Galois group of a number field ramifying only at $p$.

2010 Mathematics Subject Classification

Primary 11F11. Secondary 11F80, 11R32, 12F12.

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