We describe a new model of massless thermal bosons which predicts an hyperbolic fluctuation spectrum at low frequencies. It is found that the partition function per mode is the Euler generating function for unrestricted partitions $p(n$). Thermodynamical quantities carry a strong arithmetical structure : they are given by series with Fourier coefficients equal to summatory functions ${\sigma }_k\left(n\right)$ of the power of divisors, with $k=-1$ for the free energy, $k=0$ for the number of particles and $k=1$ for the internal energy. Low...