G. Lomadze

On the Number of Representations of Positive Integers by the Quadratic Form x₁² + ... + x₈² + 4x₉²

abstract:
An explicit exact (non asymptotic) formula is derived for the number of representations of positive integers by the quadratic form $x_1^2+\cdots+x_8^2+4x_9^2$. The way by which this formula is derived, gives us a possibility to develop a method of finding the so-called Liouville type formulas for the number of representations of positive integers by positive diagonal quadratic forms in nine variables with integral coefficients