Let $X$ be a modular curve and consider sequence of Galois orbits CM points in $X$, whose $p$-conductors tend to infinity. Its equidistribution properties $X(\mathbf{C})$ the reductions modulo primes different from $p$ are well understood. We study problem Berkovich analytification $X\_{p}^{\operatorname{an}}$ $X\_{\operatorname{Q}\_{p}}$. partition set sufficiently high conductor $X\_{\operato...

Abstract We investigate tomography of 21-cm brightness temperature fluctuations during the Dark Ages as a probe for constraining primordial non-Gaussianity. expand up to cubic order in perturbation theory and improve previous models signal by including effect free electron fraction. Using modified standard methods that include baryonic pressure effects we derive an improved secondary bispectrum...