Subconvexity of Shintani’s zeta function

Hough, Robert; Lee, Eun Hye

doi:10.1090/tran/8772

Subconvexity of Shintani’s zeta function
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by Robert D. Hough and Eun Hye Lee PDF

Trans. Amer. Math. Soc. 375 (2022), 8277-8295 Request permission

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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