Cherednik, Ivan

From double Hecke algebra to analysis

Doc. Math. (Bielefeld) Extra Vol. ICM Berlin 1998, Vol. II, 527-537 (1998)


We discuss $q$-counterparts of the Gauss integrals, a new type of Gauss-Selberg sums at roots of unity, and $q$-deformations of Riemann's zeta-function. The paper contains general results, one-dimensional formulas, and remarks about the current projects involving the double affine Hecke algebras.

Mathematics Subject Classification

11L05, 33D80, 05A30, 11M06, 20C08, 33C80


double affine Hecke algebras, Fourier transform, spherical function, Macdonald polynomial, Gauss integral, Gaussian sum, metaplectic representation, Verlinde algebra, braid group, Riemann zeta-function