Zobrazeno 1 - 10
of 797
pro vyhledávání: '"Pastén, P."'
Autor:
Pasten, Hector
We construct explicit non-isotrivial families of polynomials over $\mathbb{Q}$ satisfying uniform boundedness for their rational preperiodic points.
Externí odkaz:
http://arxiv.org/abs/2408.13262
Autor:
Pasten, Hector
One of the main open problems in the context of extensions of Hilbert's tenth problem (HTP) is the case of the ring of complex entire functions in one variable. Our main result provides a step towards an answer: For every $\rho\ge 0$, we give a negat
Externí odkaz:
http://arxiv.org/abs/2406.12791
Autor:
Pasten, Hector, Sepúlveda-Manzo, Rocío
We revisit a subexponential bound for the $abc$ conjecture due to the first author, and we establish a variation of it using linear forms in logarithms. As an application, we prove an unconditional subexponential bound towards the $4$-terms $abc$ con
Externí odkaz:
http://arxiv.org/abs/2406.05083
Autor:
Garcia-Fritz, Natalia, Pasten, Hector
Given a complex projective algebraic variety $X$ we define $ h(X)$ as the largest $n$ such that the $n$-th symmetric power of $X$ is (Brody) hyperbolic. Using Nevanlinna theory for algebroid maps, we give non-trivial lower bounds for $ h(X)$. From an
Externí odkaz:
http://arxiv.org/abs/2406.00835
We investigate the behavior of active Brownian particles (ABP) within a temporal complex network framework approach. We focused on the node degree distribution, average path length, and average clustering coefficient across the P\'eclet number and pa
Externí odkaz:
http://arxiv.org/abs/2402.03228
Autor:
Pasten, Hector
We combine transcendental methods and the modular approaches to the $ABC$ conjecture to show that the largest prime factor of $n^2+1$ is at least of size $(\log_2 n)^2/\log_3n$ where $\log_k$ is the $k$-th iterate of the logarithm. This gives a subst
Externí odkaz:
http://arxiv.org/abs/2312.03566
Autor:
Garcia-Fritz, Natalia, Pasten, Hector
We give a general criterion for Zariski degeneration of integral points in the complement of a divisor $D$ with $n$ components in a variety of dimension $n$ defined over $\mathbb{Q}$ or over a quadratic imaginary field. The key condition is that the
Externí odkaz:
http://arxiv.org/abs/2311.17701
The analogue of Hilbert's tenth problem over $\mathbb{Q}$ asks for an algorithm to decide the existence of rational points in algebraic varieties over this field. This remains as one of the main open problems in the area of undecidability in number t
Externí odkaz:
http://arxiv.org/abs/2311.01958
Autor:
Pasten, Hector
We prove Szpiro's conjecture for elliptic curves over the rationals having $j$-invariant with denominator of logarithmic size with respect to its numerator.
Comment: References updated
Comment: References updated
Externí odkaz:
http://arxiv.org/abs/2308.07114
Autor:
Garcia-Fritz, Natalia, Pasten, Hector
In the context of Hilbert's tenth problem, an outstanding open case is that of complex entire functions in one variable. A negative solution is known for polynomials (by Denef) and for exponential polynomials of finite order (by Chompitaki, Garcia-Fr
Externí odkaz:
http://arxiv.org/abs/2308.05714