# Equidistribution on the space of rank two vector bundles over the projective line

@inproceedings{Shende2013EquidistributionOT, title={Equidistribution on the space of rank two vector bundles over the projective line}, author={Vivek V. Shende and Jacob Tsimerman}, year={2013} }

Fix a finite field. A hyperelliptic curve determines a measure on the discrete space of rank two bundles on the projective line: the mass of a given vector bundle is the number of line bundles whose pushforward it is. In a sequence of hyperelliptic curves whose genera tend to infinity, these measures tend to the natural measure on the space of rank two bundles. This is a function field analogue of Duke’s theorem on the equidistribution of Heegner points, and can be proven similarly: it follows… CONTINUE READING

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