Hee Oh (Princeton University)

Hecke operators and equi-distribution of integer points on a family of homogeneous varieties.

Abstract. Let f be a homogeneous polynomial with integer coefficients, and let V_m be the variety defined by f=m. In the early sixties, Linnik raised the problem of understanding the distribution of the integer points V_m(Z) as m tends to infinity. In complete generality it seems hopeless to attack this question, except when the number of variables of f is much bigger than the degree of f in which case the Hardy-Littlewood circle method can be applied.

In this talk we discuss Linnik's problem when f arises from invariant theory, explaining how the Hecke operators then play a role here. (joint work with W. T. Gan).