Geodesic
From double Hecke algebra to analysis
Documenta mathematica, ICM Berlin 1998, Vol. II (1998), pp. 527-537.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 11L05, 33D80, 05A30, 11M06, 20C08, 33C80
Keywords: double affine Hecke algebras, Fourier transform, spherical function, Macdonald polynomial, Gauss integral, Gaussian sum, metaplectic representation, Verlinde algebra, braid group, Riemann zeta-function 
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Cherednik, Ivan. From double Hecke algebra to analysis. Documenta mathematica, ICM Berlin 1998, Vol. II (1998), pp. 527-537. http://geodesic.mathdoc.fr/item/DOCMA_1998__S8__a31/