A Symplectic Case of Artin's Conjecture
Number Theory
2014-12-30 v2
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 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.
Cite
@article{arxiv.math/0301093,
title = {A Symplectic Case of Artin's Conjecture},
author = {Kimball Martin},
journal= {arXiv preprint arXiv:math/0301093},
year = {2014}
}
Comments
Revised 13 June 2003: Corrected typographical errors, included the construction of an example in the introduction, and added a brief section at the end discussing the transfer to GSp(4)