Alex Rice

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20112023

most citedComputation on Elliptic Curves with Complex Multiplication

19 citations · 37 across the 20 of their papers we have counts for

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10 papers · 1 filter

math.NT2022

Computations and observations on congruence covering systems

Raj Agrawal, Prarthana Bhatia, Kratik Gupta +4

A $covering system$ is a collection of integer congruences such that every integer satisfies at least one congruence in the collection. A covering system is called $\texti…

math.NT2020

Multivariate Polynomial Values in Difference Sets

John R. Doyle, Alex Rice

For $ℓ \geq 2$ and $h \in Z [x_{1}, \dots, x_{ℓ}]$ of degree $k \geq 2$ , we show that every set $A \subseteq {1, 2, \dots, N}$ lacking nonzero differences in $h(\mathbb{Z}^{\e…

math.NT2018

Binary Quadratic Forms in Difference Sets

Alex Rice

We show that if $h (x, y) = a x^{2} + b x y + c y^{2} \in Z [x, y]$ satisfies $Δ (h) = b^{2} - 4 a c \neq = 0$ , then any subset of ${1, 2, \dots, N}$ lacking nonzero differences in the image of $h$ has s…

math.NT2016★ 3 cited

A Maximal Extension of the Best-Known Bounds for the Furstenberg-Sárközy Theorem

Alex Rice

We show that if $h \in Z [x]$ is a polynomial of degree $k \geq 2$ such that $h (N)$ contains a multiple of $q$ for every $q \in N$ , known as an $\textit{int…

math.NT2015

Difference Sets and Polynomials

Neil Lyall, Alex Rice

We provide upper bounds on the largest subsets of ${1, 2, \dots, N}$ with no differences of the form $h_{1} (n_{1}) + \dots + h_{ℓ} (n_{ℓ})$ with $n_{i} \in N$ or $h_1(p_1)+\cdot…

math.NT2014★ 2 cited

A Quantitative Result on Diophantine Approximation for Intersective Polynomials

Neil Lyall, Alex Rice

In this short note, we closely follow the approach of Green and Tao to extend the best known bound for recurrence modulo 1 from squares to the largest possible class of polynomials…