Zobrazeno 1 - 10
of 34
pro vyhledávání: '"Scherr, Zachary"'
Autor:
Scherr, Zachary, Thompson, Katherine
In this paper we classify all monic, quartic, polynomials $d(x)\in\mathbb{Z}[x]$ for which the Pell equation $$f(x)^2-d(x)g(x)^2=1$$ has a non-trivial solution with $f(x),g(x)\in\mathbb{Z}[x]$.
Externí odkaz:
http://arxiv.org/abs/2307.04566
Autor:
Scherr, Zachary, Thompson, Katherine
Publikováno v:
In Journal of Number Theory June 2024 259:38-56
Autor:
Brimkov, Boris, Scherr, Zachary
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 note we present the first exact algorithm for the minimum rank of an arbi
Externí odkaz:
http://arxiv.org/abs/1912.00158
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 for the partition function and by Treneer for more general Fourier coe
Externí odkaz:
http://arxiv.org/abs/1911.05799
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 curves. Coppersmith's method uses lattice basis reduction to construct
Externí odkaz:
http://arxiv.org/abs/1605.08065
Autor:
Hablicsek, Marton, Scherr, Zachary
Publikováno v:
Discrete and Computational Geometry, 55(4), 955-962, (2016)
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 result shows that if there are sufficiently many rich lines incident t
Externí odkaz:
http://arxiv.org/abs/1412.7025
Autor:
Krieger, Holly, Levin, Aaron, Scherr, Zachary, Tucker, Thomas J., Yasufuku, Yu, Zieve, Michael
Publikováno v:
Pacific J. Math. 274 (2015) 97-106
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 \bar{K}(z), Siegel's theorem implies that the image set f(K) contains
Externí odkaz:
http://arxiv.org/abs/1406.1990
Autor:
Scherr, Zachary, Zieve, Michael E.
Publikováno v:
Mathematical Research Letters 21 (2014), 1389-1406
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 construct a finite morphism f: C -> P^1 such that f ramifies at each poi
Externí odkaz:
http://arxiv.org/abs/1310.2555
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_3\Z \times\Z/n_1 n_2 n_3 n_4\Z. We are interested in knowing which gro
Externí odkaz:
http://arxiv.org/abs/1307.0863
Autor:
Scherr, Zachary, Zieve, Michael E.
Publikováno v:
Annals of Combinatorics 18 (2014), 723-729
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 Zhou introduced a definition in even characteristic which yields similar
Externí odkaz:
http://arxiv.org/abs/1302.1244