Representations of an integer by some quaternary and octonary quadratic forms

TL;DR

This paper uses modular form theory to derive formulas for counting how many ways positive integers can be represented by specific quaternary and octonary quadratic forms.

Contribution

It introduces new formulas for representation counts of integers by certain quadratic forms using modular forms theory.

Findings

Derived explicit formulas for representation numbers

Applied modular forms to quadratic form analysis

Enhanced understanding of quadratic form representations

Abstract

In this paper we consider certain quaternary quadratic forms and octonary quadratic forms and by using the theory of modular forms, we find formulae for the number of representations of a positive integer by these quadratic forms.