3 citations · 3 across the 5 of their papers we have counts for
8 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…
Elliptic analogue of irregular prime numbers for the -division fields of the curves
Naoto Dainobu, Yoshinosuke Hirakawa, Hideki Matsumura
A prime number is said to be irregular if it divides the class number of the -th cyclotomic field . In this paper, we study…
Infinitely many hyperelliptic curves with exactly two rational points: Part II
Hideki Matsumura
In the previous paper, Hirakawa and the author determined the set of rational points of a certain infinite family of hyperelliptic curves parametrized by a prime numb…
How to calculate the proportion of everywhere locally soluble diagonal hypersurfaces
Yoshinori Kanamura, Yoshinosuke Hirakawa
In this paper, we establish a strategy for the calculation of the proportion of everywhere locally soluble diagonal hypersurfaces of of fixed degree. Our strategy…
Counterexamples to the local-global principle associated with Swinnerton-Dyer's cubic form
Yoshinosuke Hirakawa
In this paper, we imitate a classical construction of a counterexample to the local-global principle of cubic forms of 4 variables which was discovered first by Swinnerton-Dyer (Ma…
Counterexamples to the local-global principle for non-singular plane curves and a cubic analogue of Ankeny-Artin-Chowla-Mordell conjecture
Yoshinosuke Hirakawa, Yosuke Shimizu
In this article, we introduce a systematic and uniform construction of non-singular plane curves of odd degrees which violate the local-global principle. Our constructio…