Langlands program

In mathematics, the Langlands program is a set of conjectures about connections between number theory and geometry. It was proposed by Robert Langlands (1967, 1970). It seeks to relate Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local fields and adeles. It was described by Edward Frenkel as the "grand unified theory of mathematics."

Automorphic Forms on GL(2) is a mathematics book by H. Jacquet and Robert Langlands (1970) where they rewrite Erich Hecke's theory of modular forms in terms of the representation theory of GL(2) over local fields and adele rings of global fields and prove the Jacquet–Langlands correspondence. A second volume by Jacquet (1972) gives an interpretation of some results by Rankin and Selberg in terms of the representation theory of GL(2) × GL(2).