Gauss type complex quadrature formulae, power moment problem and elliptic curves

Анотація

A complex-valued Borel measure w on ℂ is called n-reducible if there is a quadrature formula with n complex nodes which is exact for all polynomials of degree £ 2n - 1. A criterion of n-reducibility is given on the base of a solvability criterion for a complex power moment problem. The latter is an analytic version of a Sylvester theorem from the theory of binary form invariants. The 2-reducibility of measures w with |suppw| = 3 is closely related to the modular invariants of elliptic curves.