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pro vyhledávání: '"Thompson, Bianca"'
We determine necessary and sufficient conditions for unicritical polynomials to be dynamically irreducible over finite fields. This result extends the results of Boston-Jones and Hamblen-Jones-Madhu regarding the dynamical irreducibility of particula
Externí odkaz:
http://arxiv.org/abs/2409.10467
We construct families of locally recoverable codes with availability $t\geq 2$ using fiber products of curves, determine the exact minimum distance of many families, and prove a general theorem for minimum distance of such codes. The paper concludes
Externí odkaz:
http://arxiv.org/abs/2204.03755
For fixed integers $D \geq 0$ and $c \geq 3$, we demonstrate how to use $2$-adic valuation trees of sequences to analyze Diophantine equations of the form $x^2+D=2^cy$ and $x^3+D=2^cy$, for $y$ odd. Further, we show for what values $D \in \mathbb{Z}^
Externí odkaz:
http://arxiv.org/abs/2105.03352
Autor:
Bell, Zoë, Camero, Jasmine, Cho, Karina, Hyde, Trevor, Lu, Chieh-Mi, Miller, Rebecca, Thompson, Bianca, Zhu, Eric
Let $L_d$ be the Latt\`es map associated to the multiplication-by-$d$ endomorphism of an elliptic curve $E$ defined over a finite field $\mathbb{F}_q$. We determine the density $\delta(L_d,q)$ of periodic points for $L_d$ in $\mathbb{P}^1(\mathbb{F}_
Externí odkaz:
http://arxiv.org/abs/2103.00074
Autor:
Juul, Jamie, Krieger, Holly, Looper, Nicole, Manes, Michelle, Thompson, Bianca, Walton, Laura
Jones conjectures the arboreal representation of a degree two rational map will have finite index in the full automorphism group of a binary rooted tree except under certain conditions. We prove a version of Jones' Conjecture for quadratic and cubic
Externí odkaz:
http://arxiv.org/abs/1804.06053
Autor:
Bell, Zoë, Camero, Jasmine, Cho, Karina, Hyde, Trevor, Lu, Chieh-Mi, Thompson, Bianca, Zhu, Eric
Publikováno v:
In Journal of Number Theory September 2022 238:951-966
Akademický článek
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Autor:
Faber, Xander, Thompson, Bianca
Publikováno v:
J. Number Theory 167 (2016) 1-6; Corrigendum: J. Number Theory 169 (2016), 439-440
Using essentially only algebra, we give a proof that a cubic rational function over $\mathbb{C}$ with real critical points is equivalent to a real rational function. We also show that the natural generalization to $\mathbb{Q}_p$ fails for all $p$.
Externí odkaz:
http://arxiv.org/abs/1601.04938
Autor:
Manes, Michelle, Thompson, Bianca
We find the limiting proportion of periodic points in towers of finite fields for polynomial maps associated to algebraic groups, namely pure power maps z^d and Chebyshev polynomials.
Comment: 18 pages, 2 figures, 10 tables
Comment: 18 pages, 2 figures, 10 tables
Externí odkaz:
http://arxiv.org/abs/1301.6158
Let phi be a morphism of projective N-space defined over a number field K. We prove that there is a bound B depending only on phi such that every twist of phi has no more than B K-rational preperiodic points. (This result is analagous to a result of
Externí odkaz:
http://arxiv.org/abs/1204.4447