On limit theorems for continued fractions

It is shown that for sums of functionals of digits in continued fraction expansion the Kolmogorov-Feller weak laws of large numbers and the Khinchine-L\'evy-Feller-Raikov characterization of the domain of attraction of the normal law hold.Comment: 16 page

Search for exotic physics in double-β decays with GERDA Phase II

A search for Beyond the Standard Model double-$\beta$ decay modes of$^{76}$Ge has been performed with data collected during the Phase II of theGERmanium Detector Array (GERDA) experiment, located at Laboratori Nazionalidel Gran Sasso of INFN (Italy). Improved limits on the decays involvingMajorons have been obtained, compared to previous experiments with $^{76}$Ge,with half-life values on the order of 10$^{23}$ yr. For the first time with$^{76}$Ge, limits on Lorentz invariance violation effects in double-$\beta$decay have been obtained. The isotropic coefficient$\mathring{a}_\text{of}^{(3)}$, which embeds Lorentz violation indouble-$\beta$ decay, has been constrained at the order of $10^{-6}$ GeV. Wealso set the first experimental limits on the search for light exotic fermionsin double-$\beta$ decay, including sterile neutrinos.<br