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pro vyhledávání: '"Samuels, Charles L."'
Autor:
Samuels, Charles L.
Recent work of the author established dual representation theorems for certain vector spaces that arise in an important article of Allcock and Vaaler. These results constructed an object called a consistent map which acts like a measure on the set of
Externí odkaz:
http://arxiv.org/abs/2405.06519
Autor:
Samuels, Charles L.
A 2009 article of Allcock and Vaaler examined the vector space $\mathcal G := \overline{\mathbb Q}^\times/\overline{\mathbb Q}^\times_{\mathrm{tors}}$ over $\mathbb Q$, describing its completion with respect to the Weil height as a certain $L^1$ spac
Externí odkaz:
http://arxiv.org/abs/2306.12887
Autor:
Samuels, Charles L.
Publikováno v:
Acta Arith. 205 (2022), no.4, 341-370
Let $\overline{\mathbb Q}$ be an algebraic closure of $\mathbb Q$ and let $A$ denote the ring of algebraic integers in $\overline{\mathbb Q}$. If $\mathcal S = \overline{\mathbb Q}^\times/A^\times$ then $\mathcal S$ is a vector space over $\mathbb Q$
Externí odkaz:
http://arxiv.org/abs/2111.01012
Autor:
Carpenter, Ryan, Samuels, Charles L.
Publikováno v:
Int. J. Number Theory 17 (2021), no. 4, 973-990
For each algebraic number $\alpha$ and each positive real number $t$, the $t$-metric Mahler measure $m_t(\alpha)$ creates an extremal problem whose solution varies depending on the value of $t$. The second author studied the points $t$ at which the s
Externí odkaz:
http://arxiv.org/abs/2111.01002
Autor:
Ayub, Yemeen, Samuels, Charles L.
Suppose that $p$ is an odd prime and $\genfrac{(}{)}{}{}{\cdot}{p}$ denotes the Legendre symbol modulo $p$. If $p$ is has the form $p= n^2+1$ then one easily verifies that $\genfrac{(}{)}{}{}{a}{p} = \genfrac{(}{)}{}{}{-a}{p}$ for all $a\in \mathbb Z
Externí odkaz:
http://arxiv.org/abs/1808.06037
Autor:
Kelly, James P., Samuels, Charles L.
The ad\`ele ring $\mathbb A_K$ of a global field $K$ is a locally compact, metrizable topological ring which is complete with respect to any invariant metric on $\mathbb A_K$. For a fixed global field $F$ and a possibly infinite algebraic extension $
Externí odkaz:
http://arxiv.org/abs/1712.08112
Autor:
Samuels, Charles L.
Publikováno v:
Acta Math. Hungar. 154 (2018), no. 1, 105--123
For an algebraic number $\alpha$, the metric Mahler measure $m_1(\alpha)$ was first studied by Dubickas and Smyth in 2001 and was later generalized to the $t$-metric Mahler measure $m_t(\alpha)$ by the author in 2010. The definition of $m_t(\alpha)$
Externí odkaz:
http://arxiv.org/abs/1705.07932
Autor:
Samuels, Charles L.
Publikováno v:
Period. Math. Hungar. 75 (2017), no. 2, 221--243
If $\alpha$ is a non-zero algebraic number, we let $m(\alpha)$ denote the Mahler measure of the minimal polynomial of $\alpha$ over $\mathbb Z$. A series of articles by Dubickas and Smyth, and later by the author, develop a modified version of the Ma
Externí odkaz:
http://arxiv.org/abs/1607.02081
Autor:
Samuels, Charles L.
Publikováno v:
Monatsh. Math. (2016)
The metric Mahler measure was first studied by Dubickas and Smyth in 2001 as a means of phrasing Lehmer's conjecture in topological language. More recent work of the author examined a parametrized family of generalized metric Mahler measures that giv
Externí odkaz:
http://arxiv.org/abs/1508.01726
Autor:
Fili, Paul, Samuels, Charles L.
Publikováno v:
J. Number Theory 129 (2009), 1698--1708
Recently, Dubickas and Smyth constructed and examined the metric Mahler measure and the metric na\"ive height on the multiplicative group of algebraic numbers. We give a non-Archimedean version of the metric Mahler measure, denoted $M_\infty$, and pr
Externí odkaz:
http://arxiv.org/abs/1408.5084