Subconvexity of Shintani's zeta function

Robert Hough; Eun Hye Lee

Subconvexity of Shintani's zeta function

Number Theory 2022-06-03 v3

Authors: Robert Hough , Eun Hye Lee

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.

Keywords

subconvexity shintani zeta function prehomogeneous vector space integral orbits arithmetic statistics binary cubic forms

Cite

@article{arxiv.2104.13558,
  title  = {Subconvexity of Shintani's zeta function},
  author = {Robert Hough and Eun Hye Lee},
  journal= {arXiv preprint arXiv:2104.13558},
  year   = {2022}
}

Comments

The original paper is split into two, with the subconvexity estimate for the cusp form twisted version in a separate paper

Subconvexity of Shintani's zeta function

Abstract

Keywords

Cite

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