In mathematics, the Chowla–Mordell theorem is a result in number theory determining cases where a Gauss sum is the square root of a prime number, multiplied by a root of unity.
It was proved and published independently by Sarvadaman Chowla and Louis Mordell, around 1951.
a nontrivial Dirichlet character modulo
The 'if' part was known to Gauss: the contribution of Chowla and Mordell was the 'only if' direction.
The ratio in the theorem occurs in the functional equation of L-functions.