Product Formula of the Cubic Gauss Sum Modulo the Product of the Primes Original Research Article

Letωbe a prime in the quadratic fieldQ(e2πi/3), and letG3(ω) be the cubic Gauss sum. Matthews [Invent. Math.52(1979), 163–185;54(1979), 23–52] determined the product formula ofG3(ω) using Weierstrassʹ Weierstrass p function. In this paper, we establish an analogous result for the cubic Gauss sum modulo the product of the primes.