We prove that some new infinite families of odd two dimensional icosahedral representations of the absolute Galois group of are modular and hence satsify the Artin conjecture. We also give an account of work of Ramakrishna on lifting mod l Galois representations to characteristic zero.

American journal of mathematics

Integers; Homomorphisms; Series convergence; Prime numbers; Mathematical theorems; Algebra; Infinite series; Adjoints; Inertia; Icosahedra; Artin's conjecture; Galois theory; Exact sciences and technology; Field theory and polynomials; Mathematics; Number theory; Algebraic geometry; Sciences and techniques of general use; Research; Mathematical analysis; Langlands Tunnell theorem; Galoi representation; L function; Group theory; Isomorphism; Homomorphism; Module; Artin representation; Bearing

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