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 The non-existence of certain mod $p$ Galois representations Bull. Korean Math. Soc. 2003 Vol. 40, No. 3, 537-544 Published online September 1, 2003 Hyunsuk Moon Kyushu University Abstract : The non-existence is proved of continuous irreducible representations $\r : \Gal(\Qbar/\Q) \to \GL_2(\Fpbar)$ with Artin conductor $N$ outside $p$ for a few small values of $p$ and $N$. Keywords : mod $p$ Galois representation; Serre's conjecture; class field theory; Odlyzko's bound MSC numbers : 11F80, 11R39 Downloads: Full-text PDF