Analogues of the Ramanujan--Mordell Theorem

TL;DR

This paper extends the Ramanujan--Mordell Theorem, originally for sums of squares, to a broader class of quadratic forms and polynomials, enhancing understanding of their number-theoretic properties.

Contribution

It introduces new analogues of the Ramanujan--Mordell Theorem applicable to various quadratic forms and polynomials, expanding its scope.

Findings

Extended the theorem to new quadratic forms

Derived explicit formulas for sums involving quadratic polynomials

Enhanced understanding of quadratic form representations

Abstract

The Ramanujan--Mordell Theorem for sums of an even number of squares is extended to other quadratic forms and quadratic polynomials.