Deformations of Galois Representations and the Theorems of Sato-Tate, Lang-Trotter and others

Details Deformations of Galois Representations and the Theorems of Sato-Tate, Lang-Trotter and others Deformations of Galois Representations and the Theorems of Sato-Tate, Lang-Trotter and others

2009-08-12

arxiv.org/abs/0908.1752v2

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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