16 citations · 49 across the 11 of their papers we have counts for
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Subconvexity of twisted Shintani zeta functions
Robert Hough, Eun Hye Lee
Previously the authors proved subconvexity of Shintani's zeta function enumerating class numbers of binary cubic forms. Here we return to prove subconvexity of the Maass form twist…
Subconvexity of Shintani's zeta function
Robert Hough, Eun Hye Lee
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 enum…
Eisenstein series twisted Shintani zeta function
Robert Hough, Eun Hye Lee
We introduce the zeta function of the prehomogenous vector space of binary cubic forms, twisted by the real analytic Eisenstein series. We prove the meromorphic continuation of thi…
The local zeta function in enumerating quartic fields
Robert Hough
An exact formula is obtained for the Fourier transform of the local condition of maximality modulo primes in the prehomogeneous vector space $2 \otimes \mathrm{Sym}^2(\mathbb…
The shape of quartic fields
Robert Hough
We use the method of Shintani, as developed by Taniguchi and Thorne, to prove the joint cuspidal equidistribution of the shape of quartic fields paired with the shape of its cubic…
The shape of cubic fields
Robert Hough
We use the method of Shintani, as developed by Taniguchi and Thorne, to prove the quantitative equidistribution of the shape of cubic fields when the fields are ordered by discrimi…
Covering systems with restricted divisibility
Robert D. Hough, Pace P. Nielsen
We prove that every distinct covering system has a modulus divisible by either 2 or 3.