Computation of the number representations of the elements of the ringℤ/dℤ as a sum of squares

Abstract

The number of representations of the elements of the ringℤ/dℤ as a sum of invertible squares is computed, provided that each square occurs in the sum no more tha a fized number of times. For prime d an exhaustive answer is given in term of the class number and the fundamental unit of the real quadratic field\(\mathbb{Q}(\sqrt d )\). Biblography: 5 titles.