SUBCONVEXITY OF SHINTANI’S ZETA FUNCTION

Robert D. Hough; Eun Hye Lee

doi:10.1090/tran/8772

SUBCONVEXITY OF SHINTANI’S ZETA FUNCTION

Robert D. Hough
, Eun Hye Lee

Mathematics

Stony Brook University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 ζ function enumerating class numbers of binary cubic forms.

Original language	English
Pages (from-to)	8277-8295
Number of pages	19
Journal	Transactions of the American Mathematical Society
Volume	375
Issue number	11
DOIs	https://doi.org/10.1090/tran/8772
State	Published - Nov 1 2022

Keywords

Subconvexity
cubic ring
oscillatory integral
prehomogeneous vector space
space of lattices
zeta function

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10.1090/tran/8772

Cite this

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title = "SUBCONVEXITY OF SHINTANI{\textquoteright}S ZETA FUNCTION",

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 ζ function enumerating class numbers of binary cubic forms.",

keywords = "Subconvexity, cubic ring, oscillatory integral, prehomogeneous vector space, space of lattices, zeta function",

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N2 - 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 ζ function enumerating class numbers of binary cubic forms.

AB - 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 ζ function enumerating class numbers of binary cubic forms.

KW - Subconvexity

KW - cubic ring

KW - oscillatory integral

KW - prehomogeneous vector space

KW - space of lattices

KW - zeta function

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M3 - Article

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 11

ER -

SUBCONVEXITY OF SHINTANI’S ZETA FUNCTION

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Keywords

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