Modular forms and some cases of the inverse Galois problem

2015/08/31 by David Zywina, Zywina, David · 1 citation
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1508.07916

arxiv created 2015/08/31 · arxiv updated 2015/09/01

Abstract

We prove new cases of the inverse Galois problem by considering the residual Galois representations arising from a fixed newform. Specific choices of weight 3 newforms will show that there are Galois extensions of ℚ with Galois group PSL₂(\mathbbF_p) for all primes p and PSL₂(\mathbbF_p³) for all odd primes p ≡ ± 2, ± 3, ± 4, ± 6 \pmod13.

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