Diego Marques
Algebraic and transcendental solutions of some exponential equations.
Чт, 09/01/2011 - 15:01 — SomNambulAuthors: Diego Marques, Jonathan Sondow
Subjects: Number Theory
AbstractWe study algebraic and transcendental powers of positive real numbers,
including solutions of each of the equations $x^x=y$, $x^y=y^x$, $x^x=y^y$,
$x^y=y$, and $x^{x^y}=y$. Applications to values of the iterated exponential
functions are given. The main tools used are classical theorems of
Hermite-Lindemann and Gelfond-Schneider, together with solutions of exponential
Diophantine equations.Transcendence Measures for some $U_m$-numbers related to Liouville's constant.
Ср, 10/21/2009 - 14:15 — SomNambulAuthors: Ana Paula Chaves, Diego Marques
Subjects: Number Theory
AbstractIn this note, we shall prove that the sum and the product of an algebraic
number $\alpha$ by the \textit{Liouville constant}
$L=\sum_{j=1}^{\infty}10^{-j!}$ is a $U$-number with type equals to the degree
of $\alpha$ (with respect to $\mathbb{Q}$). Moreover, we shall have that$\max\{w^{\ast}_n(\alpha L),w^{\ast}_n(\alpha + L)\}\leq 2m^2n+m-1$, for
$n=1,...,m-1$.Transcendence Measures for some $U_m$-numbers related to Liouville's constant.
Ср, 10/21/2009 - 14:15 — SomNambulAuthors: Ana Paula Chaves, Diego Marques
Subjects: Number Theory
AbstractIn this note, we shall prove that the sum and the product of an algebraic
number $\alpha$ by the \textit{Liouville constant}
$L=\sum_{j=1}^{\infty}10^{-j!}$ is a $U$-number with type equals to the degree
of $\alpha$ (with respect to $\mathbb{Q}$). Moreover, we shall have that$\max\{w^{\ast}_n(\alpha L),w^{\ast}_n(\alpha + L)\}\leq 2m^2n+m-1$, for
$n=1,...,m-1$.
Вход в систему
