Subconvexity of Shintani's zeta function

Published 28 Apr 2021 in math.NT | (2104.13558v3)

Abstract: Enumerating integral orbits in prehomogeneous vector spaces plays an important role in arithmetic statistics. We describe a method of proving subconvexity of the zeta function enumerating the integral orbits, illustrated by proving a subconvex estimate for the Shintani $\zeta$ function enumerating class numbers of binary cubic forms.

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