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Strong Artin Conjecture for Generalized Octahedral Representations in GL3

  • Junwu Wang
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Abstract

We prove the strong Artin conjecture for the largest solvable Artin representations in three dimensions, whose projective image is isomorphic to the affine special linear group C32rtimes SL(2, 3). It is also the last solvable case in three dimensions. This is achieved with a new case of base change and automorphic induction for non-Galois quartic extensions with no intermediate fields. We additionally deduce the strong Artin conjecture for all 6-dimensional primitive solvable Artin representations.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026strong,
  title = {{Strong Artin Conjecture for Generalized Octahedral Representations in $\mathrmGL_3$}},
  author = {Junwu Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.38231},
  eprint = {2609.38231},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.38231},
}
RIS
TY  - UNPB
TI  - Strong Artin Conjecture for Generalized Octahedral Representations in GL_3
AU  - Junwu Wang
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.38231
UR  - https://arxiv.org/abs/2609.38231
AB  - We prove the strong Artin conjecture for the largest solvable Artin representations in three dimensions, whose projective image is isomorphic to the affine special linear group C_3^2rtimes SL(2, 3). It is also the last solvable case in three dimensions. This is achieved with a new case of base change and automorphic induction for non-Galois quartic extensions with no intermediate fields. We additionally deduce the strong Artin conjecture for all 6-dimensional primitive solvable Artin representations.
ER  -