Miho Aoki

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math.NT2026

Galois module structure of algebraic integers of cyclic cubic fields

Miho Aoki

We determine the Galois module structure of the ring of integers for all cubic fields using roots of the generic cyclic cubic polynomial $f_{n} (X) = X^{3} - n X^{2} - (n + 3) X - 1$ . Let $L_n=\mathb…

math.NT2025

Gaussian periods and Shanks' cubic polynomials. II

Miho Aoki

We give a linear relation between a cubic Gaussian period and a root of Shanks' cubic polynomial in wildly ramified cases.