近期，谭波教授的文章《Quantitative Diophantine approximation and Fourier dimension of sets: Dirichlet non-improvable numbers versus well-approximable numbers》在国际期刊《Advances in Mathematics》正式发表。

  摘要：Let E subset of[0,1] be a set that supports a probability measure mu with the property that |mu(t)|<<(log|t|)(-A) for some constant A>2. Let A=(q(n))(n is an element of N) be a positive, real-valued, lacunary sequence. We present a quantitative inhomogeneous Khintchine-type theorem in which the points of interest are restricted to E and the denominators of the shifted fractions are restricted to A. Our result improves and extends a previous result in this direction obtained by Pollington-Velani-Zafeiropoulos-Zorin (2022). We also show that the Dirichlet non-improvable set VS well-approximable set is of positive Fourier dimension. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

      论文链接: https://www.sciencedirect.com/science/article/pii/S000187082600109X?pes=vor&utm_source=clarivate&getft_integrator=clarivate