Number theory · Oct 6, 2026

Patterson's first moment for cubic Gauss sums

Proves unconditionally the all-primary-prime form of Patterson’s first-moment asymptotic: normalized cubic Gauss sums over primary Eisenstein primes of norm at most X, including both conjugates, have an explicit positive main term of order X5/6/log⁡XX^{5/6}/\log X. Every fixed nonzero prime-angle Fourier mode has smaller order.

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