We show that for any irrational $\alpha$ and any $\tau<8/23$ there are infinitely many $n$ which are the product of two primes for which $$\|n\alpha\|\leq n^{-\tau}.$$ We also show that for all sufficiently large $b$ there exist 3-digit palindromes in base $b$ with precisely two prime factors.
Diophantine approximation and automorphic spectrum
Quantitative non-divergence and Diophantine approximation on manifolds
Transference theorems for Diophantine approximation with weights
![QR code for arXiv:1302.6061 [math.NT]](http://oss.arxitics.com/images/favicon.svg)