Mathematics – Number Theory
Scientific paper
2009-08-12
Mathematics
Number Theory
To appear in International Journal of Number Theory
Scientific paper
We construct infinitely ramified Galois representations $\rho$ such that the
$a_l (\rho)$'s have distributions in contrast to the statements of Sato-Tate,
Lang-Trotter and others. Using similar methods we deform a residual Galois
representation for number fields and obtain an infinitely ramified
representation with very large image, generalising a result of Ramakrishna.
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