Yoshinosuke Hirakawa

activity

20182025

most citedA unique pair of triangles

13 citations · 18 across the 13 of their papers we have counts for

collaborators

13 papers

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 $q$ -th power residue symbol $(a / p)_{q}$ is defined for primes $p$ and $q$ with $p \equiv 1 mod q$ . In this paper, we generali…

math.NT2023

A note on the Diophantine equation $2 l n^{2} = 1 + q + \dots + q^{α}$ and application to odd perfect numbers

Yoshinosuke Hirakawa

Let $N$ be an odd perfect number. Then, Euler proved that there exist some integers $n, α$ and a prime $q$ such that $N = n^{2} q^{α}$ , $q ∤ n$ , and $q \equiv α \equiv 1 mod 4$ .…

math.NT2023

Galois trace forms of type $A_{n}, D_{n}, E_{n}$ for odd $n$

Riku Higa, Yoshinosuke Hirakawa

Let $p$ be an odd prime number and $ζ_{p} := exp (2 π i / p)$ . Then, it is well-known that the $A_{p - 1}$ -root lattice can be realized as the (Hermitian) trace form of the $p$ -th cyclot…

math.NT2023

Absolute zeta functions arising from ceiling and floor Puiseux polynomials

Yoshinosuke Hirakawa, Takuki Tomita

For the $Z$ -lift $X_{Z}$ of a monoid scheme $X$ of finite type, Deitmar-Koyama-Kurokawa calculated its absolute zeta function by interpolating $\#X_\mathbb{Z}(\math…

math.NT2022

Elliptic analogue of irregular prime numbers for the $p^{n}$ -division fields of the curves $y^{2} = x^{3} - (s^{4} + t^{2}) x$

Naoto Dainobu, Yoshinosuke Hirakawa, Hideki Matsumura

A prime number $p$ is said to be irregular if it divides the class number of the $p$ -th cyclotomic field $Q (ζ_{p}) = Q (G_{m} [p])$ . In this paper, we study…

math.NT2020

Primes of the form $X^{3} + N Y^{3}$ and a family of non-singular plane curves which violate the local-global principle

Yoshinosuke Hirakawa

Let $n$ be an integer such that $n = 5$ or $n \geq 7$ . In this article, we introduce a recipe for a certain infinite family of non-singular plane curves of degree $n$ which violate…

math.NT2020

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 $C^{(p; i, j)}$ parametrized by a prime numb…

math.NT2020

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 $P^{n}$ of fixed degree. Our strategy…

math.NT2019

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…

math.NT2019

Quadratic fields, Artin-Schreier extensions, and Bell numbers

Yoshinosuke Hirakawa

In this article, we prove a modulo $p$ congruence which connects the class number of the quadratic field $Q ((- 1)^{(p - 1) /2} p)$ and the trace of a certain monomial in…

math.NT2019★ 2 cited

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 $n \geq 5$ which violate the local-global principle. Our constructio…

math.NT2019★ 3 cited

Infinitely many hyperelliptic curves with exactly two rational points

Yoshinosuke Hirakawa, Hideki Matsumura

In this paper, we construct some families of infinitely many hyperelliptic curves of genus $2$ with exactly two rational points. In the proof, we first show that the Mordell-Weil r…

math.NT2018★ 13 cited

A unique pair of triangles

Yoshinosuke Hirakawa, Hideki Matsumura

A rational triangle is a triangle with sides of rational lengths. In this short note, we prove that there exists a unique pair of a rational right triangle and a rational isosceles…

A note on the second supplementary law of rational power residue symbols

A note on the Diophantine equation 2ln2=1+q+⋯+qα and application to odd perfect numbers

Galois trace forms of type An​,Dn​,En​ for odd n

Absolute zeta functions arising from ceiling and floor Puiseux polynomials

Elliptic analogue of irregular prime numbers for the pn-division fields of the curves y2=x3−(s4+t2)x

Primes of the form X3+NY3 and a family of non-singular plane curves which violate the local-global principle

Infinitely many hyperelliptic curves with exactly two rational points: Part II

How to calculate the proportion of everywhere locally soluble diagonal hypersurfaces

Counterexamples to the local-global principle associated with Swinnerton-Dyer's cubic form

Quadratic fields, Artin-Schreier extensions, and Bell numbers

Counterexamples to the local-global principle for non-singular plane curves and a cubic analogue of Ankeny-Artin-Chowla-Mordell conjecture

Infinitely many hyperelliptic curves with exactly two rational points

A unique pair of triangles

A note on the Diophantine equation $2 l n^{2} = 1 + q + \dots + q^{α}$ and application to odd perfect numbers

Galois trace forms of type $A_{n}, D_{n}, E_{n}$ for odd $n$

Elliptic analogue of irregular prime numbers for the $p^{n}$ -division fields of the curves $y^{2} = x^{3} - (s^{4} + t^{2}) x$

Primes of the form $X^{3} + N Y^{3}$ and a family of non-singular plane curves which violate the local-global principle