A Symplectic Case of Artin's Conjecture
Kimball Martin
Abstract
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 E16 be the elemetary abelian group of order 16 and C5 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 E16 by C5, 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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