2011

Uniformization, Unipotent Flows and the Riemann Hypothesis

Cacciatori, Sergio L., Cardella, Matteo A.

Understand

We prove equidistribution of certain multidimensional unipotent flows in the moduli space of genus $g$ principally polarized abelian varieties (ppav).

This is done by studying asymptotics of $\pmb{\Gamma}_{g} \sim Sp(2g,\mathbb{Z})$-automorphic forms averaged along unipotent flows, toward the codimension-one component of the boundary of the ppav moduli space.
We prove a link between the error estimate and the Riemann hypothesis.
Further, we prove $\pmb{\Gamma}_{g - r}$ modularity of the function obtained by iterating the unipotent average process $r$ times.

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