Note on a paper by A. Granville and K. Soundararajan

In this note, we improve some results of Granville and Soundararajan on the distribution of values of the truncated random Euler product L(1,X;y):=∏p⩽y(1−X−1(p)/p), where the X(p) are independent random variables, taking the values ±1 with equal probability p/2(p+1) and 0 with probability 1/(p+1).