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math.NT2019★ 1 cited
The characterization of cyclic cubic fields with power integral bases
Tomokazu Kashio, Ryutaro Sekigawa
We provide an equivalent condition for the monogenity of the ring of integers of any cyclic cubic field. We show that if a cyclic cubic field is monogenic then it is a simplest cub…
math.NT2019
Note on Coleman's formula for the absolute Frobenius on Fermat curves
Tomokazu Kashio
Coleman calculated the absolute Frobenius on Fermat curves explicitly. In this paper we show that a kind of -adic continuity implies a large part of his formula. To do this, we…