Spectral asymptotics for a family of arithmetical matrices and connection to Beurling primes

Titus Hilberdink, Alexander Pushnitski

We consider the family of arithmetical matrices given explicitly by $$E={\left\{\frac{[n,m{]}^t}{(nm{)}^{(\rho +t)/2}}\right\}}_{n,m=1}^{\infty }$$ where $[n,m]$ is the least common multiple of…