Shimura's reciprocity law

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In mathematics, Shimura's reciprocity law, introduced by Shimura (1971), describes the action of ideles of imaginary quadratic fields on the values of modular functions at singular moduli. It forms a part of the Kronecker Jugendtraum, explicit class field theory for such fields. There are also higher-dimensional generalizations.


  • Shimura, Goro (1971), Introduction to the arithmetic theory of automorphic functions, Publications of the Mathematical Society of Japan, 11, Tokyo: Iwanami Shoten, Zbl 0221.10029