A Symplectic Case of Artin's Conjecture

Details A Symplectic Case of Artin's Conjecture A Symplectic Case of Artin's Conjecture

2003-01-09

arxiv.org/abs/math/0301093v2

Mathematics

Number Theory

Revised 13 June 2003: Corrected typographical errors, included the construction of an example in the introduction, and added a

Scientific paper

Let K/F be an arbitrary Galois extension of number fields and r be a representation of Gal(K/F) into GSp(4,C). Let E_16 be the elemetary abelian group of order 16 and C_5 the cyclic group of order 5. If the image of r in the projective space PGSp(4,C) is isomorphic to the semidirect product of E_16 by C_5, then we show r satisfies Artin's conjecture by proving r corresponds to an automorphic representation. A specific case is given where r is primitive, so Artin's conjecture does not follow from previous results.

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