Estimating the rate of successful Diophantine approximations

Abstract: Diophantine approximation studies how well real numbers can be approximated by rational numbers. Previous theorems, such as Khintchine’s theorem and the Duffin-Schaeffer conjecture, have implied that the inequalities |x-p/q| < a/q2, with p/q being Farey fractions, can accept infinitely many solutions for almost every x within the interval [0,1]. Our project studies a pertinent … Read more