Selberg's Conjectures and Artin L-functions

  title={Selberg's Conjectures and Artin L-functions},
  author={Ram Murty},
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 "Himalayan peaks" that hold the secrets of these nonabelian reciprocity laws challenge humanity, and, with the visionary Langlands program, we… CONTINUE READING
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