The number of representations of a positive integer by certain octonary quadratic forms

Abstract

The number of representations of a positive integer by each of the octonary quadratic forms x2 1 +x2 2 +3x2 3 +3x2 4 +3x2 5 + 3x2 6 + 3x2 7 + 3x2 8, x2 1 + x2 2 +x2 3 +x2 4 + 3x2 5 +3x2 6 +3x2 7 + 3x2 8, x2 1 + x2 2 + x2 3 + x2 4 + x2 5 + x2 6 + 3x2 7 + 3x2 8is determined