Energy of zeros of random sections on Riemann surfaces Qi Zhong 53C5646N30random zerosrandom sections The purpose of this paper is to determine the asymptotic of the average energy of a configuration of $N$ zeros of a system of random polynomials of degree $N$ as $N \to \infty$ and more generally the zeros of random holomorphic sections of a line bundle $L\to M$ over any Riemann surface $M$. We also compare our results to the well-known minimum of energies. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3329 10.1512/iumj.2008.57.3329 en Indiana Univ. Math. J. 57 (2008) 1753 - 1780 state-of-the-art mathematics http://iumj.org/access/