Zobrazeno 1 - 10
of 1 689
pro vyhledávání: '"THOMPSON, KATHERINE"'
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
Let $f(t_1,\ldots,t_n)$ be a nondegenerate integral quadratic form. We analyze the asymptotic behavior of the function $D_f(X)$, the number of integers of absolute value up to $X$ represented by $f$. When $f$ is isotropic or $n$ is at least $3$, we s
Externí odkaz:
http://arxiv.org/abs/2304.07399
Autor:
Price, Geoffrey, Thompson, Katherine
For any finite field $\mathbb{F}$ and any positive integer $n$ we count the number of monic polynomials of degree $n$ over $\mathbb{F}$ with nonzero constant coefficient and a self-reciprocal factor of any specified degree. An application is given fo
Externí odkaz:
http://arxiv.org/abs/2210.15703
Autor:
Rainear, Benjamin, Thompson, Katherine
Mordell in 1958 gave a new proof of the three squares theorem. Those techniques were generalized by Blackwell, et al., in 2016 to characterize the integers represented by the remaining six "Ramanujan-Dickson ternaries". We continue the generalization
Externí odkaz:
http://arxiv.org/abs/2206.00589
Autor:
Rouse, Jeremy, Thompson, Katherine
Let $Q$ be a positive-definite quaternary quadratic form with prime discriminant. We give an explicit lower bound on the number of representations of a positive integer $n$ by $Q$. This problem is connected with deriving an upper bound on the Peterss
Externí odkaz:
http://arxiv.org/abs/2206.00412
Autor:
Thompson, Katherine, White, Marney A., Schrag, Ruby, Lavender, Jason M., Bauman, Viviana, Mains, Autumn, Rioux, Stephanie, Spinner, Holly, Thorstad, Isabel, Klein, David, Haigney, Mark, Tanofsky-Kraff, Marian
Publikováno v:
In Appetite 1 December 2024 203
