Abstract In this paper, we study the value distributions of L-functions holomorphic primitive cusp forms in level aspect. We associate such automorphic with probabilistic models called random Euler products. First, prove existence probability density functions attached to Then various mean values are expressed as integrals involving functions. Moreover, estimate discrepancies between and those

we propose a wavelet based regression function estimator for the estimation of the regression function for a sequence of ?-missing random variables with a common one-dimensional probability density function. some asymptotic properties of the proposed estimator based on block thresholding are investigated. it is found that the estimators achieve optimal minimax convergence rates over large class...

In this work, we studied the impact of galaxy morphology on photometric redshift (photo-$z$) probability density functions (PDFs). By including morphological parameters like radius, axis-ratio, surface brightness and S\'ersic index in addition to $ugriz$ broadbands as input parameters, used machine learning photo-$z$ algorithm ANNz2 train test galaxies from Canada-France-Hawaii Telescope Stripe...