1 citations · 2 across the 6 of their papers we have counts for
9 papers
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…
Minimal relative units of the cyclotomic -extension
Tomokazu Kashio, Hyuga Yoshizaki
Let . For the relative norm map …
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…
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…
On a common refinement of Stark units and Gross-Stark units
Tomokazu Kashio
The purpose of this paper is to formulate and study a common refinement of a version of Stark's conjecture and its -adic analogue, in terms of Fontaine's -adic period ring an…
-adic measures associated with zeta values and -adic multiple gamma functions
Tomokazu Kashio
We study a relation between two refinements of the rank one abelian Gross-Stark conjecture: For a suitable abelian extension of number fields, a Gross-Stark unit is defined a…
On the ratios of Barnes' multiple gamma functions to the -adic analogues
Tomokazu Kashio
Let be a totally real field. For each ideal class of and each real embedding of , Hiroyuki Yoshida defined an invariant as a finite sum of log of Barnes…
On the algebraicity of some products of special values of Barnes' multiple gamma function
Tomokazu Kashio
We consider partial zeta functions associated with ray classes 's of a totally real field. Stark's conjecture implies that an appropriate product of 's i…
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…