On some applications of a theorem of Worley (CROSBI ID 573923)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija
Podaci o odgovornosti
Jadrijević, Borka
engleski
On some applications of a theorem of Worley
The following result of Worley and Dujella extends classical results of Legendere and Fatou concerning Diophantine approximations of the form |alpha - a/b| < 1/2b^2 and |alpha - a/b| < 1/b^2: Let alpha be a real number and a and b coprime nonzero integers, satisfying the inequality |alpha - a/b| < M/b^2 ; where M is a positive real number. Then (a, b) = (rp_{;n+1}; +- up_n, rq_{;n+1}; +- uq_n), for some n >= -1 and nonnegative integers r and u such that ru < 2M ; where p_n=q_n denotes the n-th convergent of alpha. This result is very useful for solving various types of problems that can be reduced to solving a parametric Pellian equation or a system of the parametric Pellian equations with bounded right hand side. In this talk we will present a few results obtained in this way.
diophantine approximations; continued fractions; Thue equations
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
Podaci o prilogu
54-54.
2011.
objavljeno
Podaci o matičnoj publikaciji
27th Journees Arithmetiques
Vilnius: Vilnius University
Podaci o skupu
27th Journees Arithmetiques
predavanje
27.06.2011-01.07.2011
Vilnius, Litva