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math.NT2024
The constructive inverse Galois problem via Hilbert modular forms: realizing the transitive group 17T7
Raymond van Bommel, Edgar Costa, Noam D. Elkies +3
We show how Hilbert modular forms can be used in the constructive inverse Galois problem over the rationals. In particular, we prove that the transitive permutation group 17T7, iso…
math.NT2024
Reduction of Plane Quartics and Dixmier-Ohno invariants
Raymond van Bommel, Jordan Docking, Reynald Lercier +1
We characterise, in terms of Dixmier-Ohno invariants, the types of singularities that a plane quartic curve can have. We then use these results to obtain new criteria for determini…