Artin conjecture on Artin $L$-functions asserts that the Artin $L$-function $L(\rho,s)$ of a non-trivial irreducible representation $\rho$ of the Galois group $\Gamma$ of a number field admits analytic continuation to the whole complex plane.

It is known for $1$-dimensional and induced representations, plus a few other special cases.

What is the status towards a proof? References would be very much appreciated.

Langlands, R. P. (1970), "Problems in the theory of automorphic forms", Lectures in modern analysis and applications, III, Lecture Notes in Math 170, Berlin, New York: Springer-Verlag, pp. 18–61.

Artin conjecture on Artin $L$-functions asserts that the Artin $L$-function $L(\rho,s)$ of a non-trivial irreducible representation $\rho$ of the Galois group $\Gamma$ of a number field admits analytic continuation to the whole complex plane.

It is known for $1$-dimensional and induced representations, plus a few other special cases.

What is the status towards a proof? References would be very much appreciated.

Langlands, R. P. (1970), "Problems in the theory of automorphic forms", Lectures in modern analysis and applications, III, Lecture Notes in Math 170, Berlin, New York: Springer-Verlag, pp. 18–61.

Artin's conjecture on Artin $L$-functions asserts that the Artin $L$-function $L(\rho,s)$ of a non-trivial irreducible representation $\rho$ of the Galois group of a number field admits analytic continuation to the whole complex plane.

It is known for $1$-dimensional and induced representations, plus a few other special cases.

What is the status towards a proof? References would be very much appreciated.

Langlands, R. P. (1970), "Problems in the theory of automorphic forms", Lectures in modern analysis and applications, III, Lecture Notes in Math 170, Berlin, New York: Springer-Verlag, pp. 18–61.

Artin conjecture on Artin $L$-functions asserts that the Artin $L$-function $L(\rho,s)$ of a non-trivial irreducible representation $\rho$ of the Galois group $\Gamma$ of a number field admits analytic continuation to the whole complex plane.

It is known for $1$-dimensional and induced representations, plus a few other special cases.

What is the status towards a proof? References would be very much appreciated.

Langlands, R. P. (1970), "Problems in the theory of automorphic forms", Lectures in modern analysis and applications, III, Lecture Notes in Math 170, Berlin, New York: Springer-Verlag, pp. 18–61.