An algebraic approach to count the number of representations of an integer by the quadratic form $x^2+a{y}^2$ for certain values of $a$

Thanathat Dechakulkamjorn, Nithi Rungtanapirom

By considering the norm of elements in the ring of integers in $\mathbb{Q}(\sqrt{-a})$, we give an algebraic approach to count the number of integral solutions of diophantine equat…