10 citations · 30 across the 7 of their papers we have counts for
9 papers
Quartic Integral Polynomial Pell Equations
Zachary Scherr, Katherine Thompson
In this paper we classify all monic, quartic, polynomials for which the Pell equation has a non-trivial solution with $f(x),g(x)\in\m…
An exact algorithm for the minimum rank of a graph
Boris Brimkov, Zachary Scherr
The minimum rank of a graph G is the minimum rank over all real symmetric matrices whose off-diagonal sparsity pattern is the same as that of the adjacency matrix of G. In this not…
Congruences satisfied by eta-quotients
Nathan C. Ryan, Zachary Scherr, Nicolás Sirolli +1
The values of the partition function, and more generally the Fourier coefficients of many modular forms, are known to satisfy certain congruences. Results given by Ahlgren and Ono…
Cryptographic applications of capacity theory: On the optimality of Coppersmith's method for univariate polynomials
Ted Chinburg, Brett Hemenway, Nadia Heninger +1
We draw a new connection between Coppersmith's method for finding small solutions to polynomial congruences modulo integers and the capacity theory of adelic subsets of algebraic c…
On the number of rich lines in high dimensional real vector spaces
Marton Hablicsek, Zachary Scherr
In this short note we use the polynomial partitioning lemma to strengthen a recent result of Dvir and Gopi about the number of rich lines in high dimensional Euclidean spaces. Our…
Uniform Boundedness of S-Units in Arithmetic Dynamics
Holly Krieger, Aaron Levin, Zachary Scherr +3
Let K be a number field and let S be a finite set of places of K which contains all the Archimedean places. For any f(z) in K(z) of degree d at least 2 which is not a d-th power in…
Separated Belyi Maps
Zachary Scherr, Michael E. Zieve
We construct Belyi maps having specified behavior at finitely many points. Specifically, for any curve C defined over Q-bar, and any disjoint finite subsets S, T in C(Q-bar), we co…
Abelian surfaces over finite fields with prescribed groups
Chantal David, Derek Garton, Zachary Scherr +3
Let A be an abelian surface over F_q, the field of q elements. The rational points on A/\F_q form an abelian group A(\F_q) \simeq \Z/n_1\Z \times \Z/n_1 n_2 \Z \times \Z/n_1 n_2 n_…
Some planar monomials in characteristic 2
Zachary Scherr, Michael E. Zieve
Planar functions over finite fields give rise to finite projective planes and other combinatorial objects. They were originally defined only in odd characteristic, but recently Zho…