16 citations · 49 across the 11 of their papers we have counts for
12 papers
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…
Solution of the 15 puzzle problem
Yang Chu, Robert Hough
A generalized ` puzzle' consists of an numbered grid, with one missing number. A move in the game switches the position of the empty square with the position of on…
The spectrum of the abelian sandpile model
Robert Hough, Hyojeong Son
In their previous work, the authors studied the abelian sandpile model on graphs constructed from a growing piece of a plane or space tiling, given periodic or open boundary condit…
Cut-off for sandpiles on tiling graphs
Robert Hough, Hyojeong Son
Sandpile dynamics are considered on graphs constructed from periodic plane and space tilings by assigning a growing piece of the tiling either torus or open boundary conditions. A…
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 local limit theorem on nilpotent Lie groups
Robert Hough
A local limit theorem is proven on connected, simply connected nilpotent Lie groups, for a class of generating measures satisfying a moment condition and a condition on the charact…
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.
Sandpiles on the square lattice
Bob Hough, Dan Jerison, Lionel Levine
We give a non-trivial upper bound for the critical density when stabilizing i.i.d. distributed sandpiles on the lattice . We also determine the asymptotic spectral ga…