Results 11 to 20 of about 443 (25)

SPECIAL CURVES AND POSTCRITICALLY FINITE POLYNOMIALS

Forum of Mathematics, Pi, 2013
We study the postcritically finite maps within the moduli space of complex polynomial dynamical systems. We characterize rational curves in the moduli space containing an infinite number of postcritically finite maps, in terms of critical orbit relations,
MATTHEW BAKER, LAURA DE MARCO
doaj   +1 more source

NON-ARCHIMEDEAN YOMDIN–GROMOV PARAMETRIZATIONS AND POINTS OF BOUNDED HEIGHT

Forum of Mathematics, Pi, 2015
We prove an analog of the Yomdin–Gromov lemma for $p$-adic definable sets and more broadly in a non-Archimedean definable context. This analog keeps track of piecewise approximation by Taylor polynomials, a nontrivial aspect in the totally disconnected ...
RAF CLUCKERS, GEORGES COMTE, FRANÇOIS LOESER   +2 more
doaj   +1 more source

Bounding the $j$-invariant of integral points on certain modular curves

, 2014
In this paper, we obtain two effective bounds for the $j$-invariant of integral points on certain modular curves which has positive genus and less than three ...
Sha, Min
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Lower Bounds for the Canonical Height of a Unicritical Polynomial and Capacity

Forum of Mathematics, Sigma
In a recent breakthrough, Dimitrov [Dim] solved the Schinzel–Zassenhaus conjecture. We follow his approach and adapt it to certain dynamical systems arising from polynomials of the form $T^p+c$ , where p is a prime number and where the orbit of
P. Habegger, H. Schmidt
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Lower Bounds for Heights in Relative Galois Extensions

, 2017
The goal of this paper is to obtain lower bounds on the height of an algebraic number in a relative setting, extending previous work of Amoroso and Masser.
CJ Smyth, CL Stewart, D. H. Lehmer, E Dobrowolski, Emmanuel Delsinne, F Amoroso, F Amoroso, F Amoroso, F Amoroso, HM Stark, JB Friedlander, JB Rosser, N Berry, P Pollack, P Voutier, PE Blanksby, Peter Borwein, R Breusch, S Friedland   +18 more
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Canonical heights for abelian group actions of maximal dynamical rank

Forum of Mathematics, Sigma
Let X be a smooth projective variety of dimension $n\geq 2$ and $G\cong \mathbf {Z}^{n-1}$ a free abelian group of automorphisms of X over $\overline {\mathbf {Q}}$ . Suppose that G is of positive entropy.
Fei Hu, Guolei Zhong
doaj   +1 more source

CM relations in fibered powers of elliptic families

, 2017
Let $E_\lambda$ be the Legendre family of elliptic curves. Given $n$ linearly independent points $P_1,\dots , P_n \in E_\lambda\left(\overline{\mathbb{Q}(\lambda)}\right)$ we prove that there are at most finitely many complex numbers $\lambda_0$ such ...
André, Bombieri, David, Fabrizio Barroero, Ford, Habegger, Lang, Masser, Pila, Silverman, Zannier   +10 more
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Integral orthogonal bases of small height for real polynomial spaces [PDF]

, 2009
Let $P_N(R)$ be the space of all real polynomials in $N$ variables with the usual inner product $$ on it, given by integrating over the unit sphere. We start by deriving an explicit combinatorial formula for the bilinear form representing this inner ...
Fukshansky, Lenny
core   +3 more sources

Average Analytic Ranks of Elliptic Curves over Number Fields

Forum of Mathematics, Sigma
We give a conditional bound for the average analytic rank of elliptic curves over an arbitrary number field. In particular, under the assumptions that all elliptic curves over a number field K are modular and have L-functions which satisfy the ...
Tristan Phillips
doaj   +1 more source

Improvements on dimension growth results and effective Hilbert’s irreducibility theorem

Forum of Mathematics, Sigma
We sharpen and generalize the dimension growth bounds for the number of points of bounded height lying on an irreducible algebraic variety of degree d, over any global field.
Raf Cluckers, Pierre Dèbes, Yotam I. Hendel, Kien Huu Nguyen, Floris Vermeulen   +4 more
doaj   +1 more source