Arithmetic of quaternions and Eisenstein series

In the paper one computes the Fourier coefficients of the Eisenstein series of the orthogonal group of signature $(1,4)$. The formulas show that the restriction of the Eisenstein series to the “imaginary” axis is a Dirichlet series, whose coefficients are the products of the $L$-series by the number of the representations of the given number as a sum of three squares.