Modular forms applied to the computational inverse Galois problem

Details Modular forms applied to the computational inverse Galois problem Modular forms applied to the computational inverse Galois problem

2011-09-30

arxiv.org/abs/1109.6879v1

Mathematics

Number Theory

13 pages

Scientific paper

For each of the groups PSL2(F25), PSL2(F32), PSL2(F49), PGL2(F25), and PGL2(F27), we display the first explicitly known polynomials over Q having that group as Galois group. Each polynomial is related to a Galois representation associated to a modular form. We indicate how computations with modular Galois representations were used to obtain these polynomials. For each polynomial, we also indicate how to use Serre's conjectures to determine the modular form giving rise to the related Galois representation.

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