Geodesic
Gauss type complex quadrature formulae, power moment problem and elliptic curves
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2002) no. 2, pp. 128-145 Cet article a éte moissonné depuis la source Math-Net.Ru

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A complex-valued Borel measure $\omega$ on $\mathbb C$ is called $n$-reducible if there is a quadrature formula with $n$ complex nodes which is exact for all polynomials of degree $\le 2n-1$. 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 $\omega$ with $|{\mathrm{supp}\,\omega}|=3$ is closely related to the modular invariants of elliptic curves. 
@article{JMAG_2002_9_2_a1,
     author = {Yuri I. Lyubich},
     title = {Gauss type complex quadrature formulae, power moment problem and elliptic curves},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {128--145},
     year = {2002},
     volume = {9},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2002_9_2_a1/}
}
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Yuri I. Lyubich. Gauss type complex quadrature formulae, power moment problem and elliptic curves. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2002) no. 2, pp. 128-145. http://geodesic.mathdoc.fr/item/JMAG_2002_9_2_a1/