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math.NT2025
A note on the second supplementary law of rational power residue symbols
Yoshinosuke Hirakawa, Tomokazu Kashio, Ryutaro Sekigawa +2
As a natural generalization of the Legendre symbol, the -th power residue symbol is defined for primes and with . In this paper, we generali…
math.NT2019
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.NT2015
Fermat curves and the reciprocity law on cyclotomic units
Tomokazu Kashio
We define a "period ring-valued beta function" and give a reciprocity law on its special values. The proof is based on some results of Rohrlich and Coleman concerning Fermat curves…