All Questions

The following is a problem we were unable to prove and left stated in the paper "Arithmetical properties of a sequence arising from an arctangent sum", J. Numb. Theory 128 (2008) 1807–1846. Define ...

The distribution $\nu_{\lambda}$ of the random series $\sum\pm\lambda^n$ is the infinite convolution product of $\frac12(\delta_{-\lambda^n}+\delta_{\lambda^n})$. This problem has been studied ...

Problem 1 Given a irrational number $\alpha$ and two polynomials with positive integer coefficients $P(n),Q(n)$, is it possible to get the asymptotic estimate and reasonable error term for: $$\...

Question I am making a tree using the following two functions: $$f(x)=\frac{x}{r},\quad g(x)=\frac{x+b}{r}$$ where $1<r<2$ and $0<b$ are rationals. Everything is a real number here. The ...