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pro vyhledávání: '"Silverman, Joseph"'
Autor:
Silverman, Joseph H.
In this note we give an overview of various quantities that are used to measure the complexity of an algebraic dynamical system f:X-->X, including the dynamical degree d(f), which gives a coarse measure of the geometric complexity of the iterates of
Externí odkaz:
http://arxiv.org/abs/2408.01559
Autor:
Silverman, Joseph H.
Let $\mathbb{F}$ be the function field of a curve over an algebraically closed field with $\operatorname{char}(\mathbb{F})\ne2,3$, and let $E/\mathbb{F}$ be an elliptic curve. Then for all finite extensions $\mathbb{K}/\mathbb{F}$ and all non-torsion
Externí odkaz:
http://arxiv.org/abs/2402.14771
Autor:
Pasten, Hector, Silverman, Joseph H.
Let $X/K$ be a smooth projective variety defined over a number field, and let $f:X\to{X}$ be a morphism defined over $K$. We formulate a number of statements of varying strengths asserting, roughly, that if there is at least one point $P_0\in{X(K)}$
Externí odkaz:
http://arxiv.org/abs/2307.12097
Autor:
Hindes, Wade, Silverman, Joseph H.
Publikováno v:
Pacific J. Math. 325 (2023) 281-297
Let $V$ be a projective variety defined over a number field $K$, let $S$ be a polarized set of endomorphisms of $V$ all defined over $K$, and let $P\in V(K)$. For each prime $\mathfrak{p}$ of $K$, let $m_{\mathfrak{p}}(S,P)$ denote the number of poin
Externí odkaz:
http://arxiv.org/abs/2303.14819
Autor:
Silverman, Joseph H.
Charles, Goren, and Lauter [J. Cryptology 22(1), 2009] explained how one can construct hash functions using expander graphs in which it is hard to find paths between specified vertices. The set of solutions to the classical Markoff equation $X^2+Y^2+
Externí odkaz:
http://arxiv.org/abs/2211.08511
Let $\mathcal{W}\subset\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^1$ be a surface given by the vanishing of a $(2,2,2)$-form. These surfaces admit three involutions coming from the three projections $\mathcal{W}\to\mathbb{P}^1\times\mathbb{P}^1$,
Externí odkaz:
http://arxiv.org/abs/2201.12588
Let $K$ be a 1-dimensional function field over an algebraically closed field of characteristic $0$, and let $A/K$ be an abelian surface. Under mild assumptions, we prove a Lehmer-type lower bound for points in $A(\bar{K})$. More precisely, we prove t
Externí odkaz:
http://arxiv.org/abs/2108.09577