Arithmetic properties of periodic points of quadratic maps

Patrick Morton

Displaying similar documents to “Arithmetic properties of periodic points of quadratic maps”

The Diophantine equation f(x) = g(y)

Yuri Bilu, Robert Tichy (2000)

Acta Arithmetica

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On three questions concerning $0, 1$ -polynomials

Michael Filaseta, Carrie Finch, Charles Nicol (2006)

Journal de Théorie des Nombres de Bordeaux

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We answer three reducibility (or irreducibility) questions for $0, 1$ -polynomials, those polynomials which have every coefficient either $0$ or $1$ . The first concerns whether a naturally occurring sequence of reducible polynomials is finite. The second is whether every nonempty finite subset of an infinite set of positive integers can be the set of positive exponents of a reducible $0, 1$ -polynomial. The third is the analogous question for exponents of irreducible $0, 1$ -polynomials.

Cycles of polynomials in algebraically closed fields of positive characteristic (II)

T. Pezda (1996)

Colloquium Mathematicae

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Set of Points on Elliptic Curve in Projective Coordinates

Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama (2011)

Formalized Mathematics

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In this article, we formalize a set of points on an elliptic curve over GF(p). Elliptic curve cryptography [10], whose security is based on a difficulty of discrete logarithm problem of elliptic curves, is important for information security.

Thomas’ conjecture over function fields

Volker Ziegler (2007)

Journal de Théorie des Nombres de Bordeaux

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Thomas’ conjecture is, given monic polynomials $p_{1},$ $..., p_{d} \in ℤ [a]$ with $0 < deg p_{1} < \dots < deg p_{d}$ , then the Thue equation (over the rational integers) $(X - p_{1} (a) Y) \dots (X - p_{d} (a) Y) + Y^{d} = 1$ has only trivial solutions, provided $a \geq a_{0}$ with effective computable $a_{0}$ . We consider a function field analogue of Thomas’ conjecture in case of degree $d = 3$ . Moreover we find a counterexample to Thomas’ conjecture for $d = 3$ .

Ideal class groups, Hilbert’s irreducibility theorem, and integral points of bounded degree on curves

Aaron Levin (2007)

Journal de Théorie des Nombres de Bordeaux

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We study the problem of constructing and enumerating, for any integers $m, n > 1$ , number fields of degree $n$ whose ideal class groups have “large" $m$ -rank. Our technique relies fundamentally on Hilbert’s irreducibility theorem and results on integral points of bounded degree on curves.

Displaying similar documents to “Arithmetic properties of periodic points of quadratic maps”

The Diophantine equation f(x) = g(y)

On three questions concerning 0 , 1 -polynomials

Cycles of polynomials in algebraically closed fields of positive characteristic (II)

Set of Points on Elliptic Curve in Projective Coordinates

Thomas’ conjecture over function fields

Ideal class groups, Hilbert’s irreducibility theorem, and integral points of bounded degree on curves

On three questions concerning $0, 1$ -polynomials