MMN-1955
Representation numbers by sums of quadratic forms $x_{1}^{2}+x_{1}x_{2}+x_{2}^{2}$ in sixteen variables
Bülent Köklüce; Müberra Gürel;Abstract
Let R(a₁,...,a₈;n) denote the number of representations of an integer n by the form a₁(x₁²+x₁x₂+x₂²)+a₂(x₃²+x₃x₄+x₄²)+a₃(x₅²+x₅x₆+x₆²)+a₄(x₇²+x₇x₈+x₈²)+a₅(x₉²+x₉x₁₀+x₁₀²)+a₆(x₁₁²+x₁₁x₁₂+x₁₂²)+a₇(x₁₃²+x₁₃x₁₄+x₁₄²)+a₈(x₁₅²+x₁₅x₁₆+x₁₆²). In this article we derive formulae for R(1,2,2,2,2,2,2,2;n), R(1,1,1,2,2,2,2,2;n), R(1,1,1,1,1,2,2,2;n) and R(1,1,1,1,1,1,1,2;n). These formulae are given in terms of the function σ₇(n) and the numbers τ_{8,2}(n) and τ_{8,6}(n).
Vol. 18 (2017), No. 1, pp. 277-283