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pro vyhledávání: '"Hamblen, Spencer"'
Autor:
Anthony, Lucas, Burton, Joe, Deegbe, Irene, England, Sarah, Hamblen, Spencer, Knowles, Reagan, Stewart, Sarah, Wright, Hannah
Let $p$ be prime and $e,k$ be positive integers, and let $R = {\mathbb Z}_p[\sqrt[e]{p}]$. We calculate the Waring numbers $g_R(k)$ for many values of $p, e$, and $k$, and investigate how the Waring numbers for $p=2$ change as $e$ and $k$ vary.
Externí odkaz:
http://arxiv.org/abs/2407.14624
Autor:
Hamblen, Spencer, Jones, Rafe
Given a field $K$, a rational function $\phi \in K(x)$, and a point $b \in \mathbb{P}^1(K)$, we study the extension $K(\phi^{-\infty}(b))$ generated by the union over $n$ of all solutions to $\phi^n(x) = b$, where $\phi^n$ is the $n$th iterate of $\p
Externí odkaz:
http://arxiv.org/abs/2211.02087
Publikováno v:
Involve 14 (2021) 783-792
We use a representability theorem of G. L. Watson to examine sums of squares in Quaternion rings with integer coefficients. This allows us to determine a large family of such rings where every element expressible as the sum of squares can be written
Externí odkaz:
http://arxiv.org/abs/2011.02118
Akademický článek
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We investigate a version of Waring's Problem over quaternion rings, focusing on cubes in quaternion rings with integer coefficients. We determine the global upper and lower bounds for the number of cubes necessary to represent all such quaternions.
Externí odkaz:
http://arxiv.org/abs/1910.02485
Lagrange's Four Squares Theorem states that any positive integer can be expressed as the sum of four integer squares. We investigate the analogous question over Quaternion rings, focusing on squares of elements of Quaternion rings with integer coeffi
Externí odkaz:
http://arxiv.org/abs/1610.07227
Publikováno v:
Int. Math. Res. Not. 2018, no. 19, 5974-5994
Let $K$ be a field complete with respect to a discrete valuation $v$ of residue characteristic $p$. Let $f(z) \in K[z]$ be a separable polynomial of the form $z^\ell-c.$ Given $a \in K$, we examine the Galois groups and ramification groups of the ext
Externí odkaz:
http://arxiv.org/abs/1610.04969
Publikováno v:
Int. Math. Res. Not. 2015(7), 1924-1958
Given a polynomial f(z) = z^d + c over a global field K and a_0 in K, we study the density of prime ideals of K dividing at least one element of the orbit of a_0 under f. The density of such sets for linear polynomials has attracted much study, and t
Externí odkaz:
http://arxiv.org/abs/1303.6513
Autor:
Hamblen, Spencer, Ramakrishna, Ravi
Publikováno v:
American Journal of Mathematics, 2008 Aug 01. 130(4), 913-944.
Externí odkaz:
https://www.jstor.org/stable/40068164
Akademický článek
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