Selberg's Conjectures and Artin L-functions


In its comprehensive form, an identity between an automorphic L-function and a "motivic" L-function is called a reciprocity law. The celebrated Artin reciprocity law is perhaps the fundamental example. The conjecture of ShimuraTaniyama that every elliptic curve over Q is "modular" is certainly the most intriguing reciprocity conjecture of our time. The… (More)