國立清華大學 數學系

Abstract Originally predicted by Ramanujan in 2016 for the discriminant function, the Ramanujan conjecture is a very deep statement concerning the size of the Fourier coefficients of cusp forms. The generalized Ramanujan conjecture expects that a generic cuspidal irreducible unitary automorphic representation of a reductive group over a global field should be locally tempered. While this conjecture is largely open, it is established for certain cases. In this survey talk we shall review the current status of this conjecture and explain some novel applications of the proven cases to explicitly construct Ramanujan graphs and Ramanujan complexes, uniformly distributed points on spheres, and Golden Gate sets in quantum computing.