On the Representations of a Positive Integer by Certain Classes of Quadratic Forms in Eight Variables

Abstract

In this paper we use the theory of modular forms to find formulas for the number of representations of a positive integer by certain class of quadratic forms in eight variables, viz.

On the number of representations by certain octonary quadratic forms with coefficients 1, 2, 3, 4 and 6

“…Therefore, from our construction it is easy to get bases for the modular form spaces M 4 (Γ 0 (24), χ), where χ is either the trivial character modulo 24 or χ = χ m , m = 8, 12 or 24. In our work [22], we used the above bases of M 4 (Γ 0 (24), χ) to find formulas for the representation numbers of a positive integer by certain classes of quadratic forms in 8 variables.…”

“…In our work [22], we used the above bases of M 4 (Γ 0 (24), χ) to find formulas for the representation numbers of a positive integer by certain classes of quadratic forms in 8 variables.…”