Deformations of Galois Representations and the Theorems of Sato-Tate, Lang-Trotter and others
Abstract
We construct infinitely ramified Galois representations such that the al ()'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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