Evaluation of some convolution sums and representation of integers by certain quadratic forms in 12 variables

Abstract

In this paper, the convolution sums [Formula: see text], [Formula: see text] [Formula: see text] and [Formula: see text] are evaluated for all [Formula: see text] and their evaluations are used to determine the number of representation of a positive integer [Formula: see text] by the forms [Formula: see text] and [Formula: see text]