Fourier series and Diophantine approximation

Han Yu (University of St Andrews)

Frank Adams 1,

Duffin-Schaeffer conjecture concerns approximating real numbers by rationals in lowest form. It is an important topic in Diophantine approximation. Although no solution of this conjecture has been found, there are some partial results proving some weaker forms by strengthening some conditions in the statement of this conjecture. Here, in this talk, we shall see that we can use Fourier analysis to make a tiny step forward and show that the Duffin-Schaeffer conjecture holds under extra logarithmic divergence and logarithmic Vaaler type upper bound.

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