13 citations · 21 across the 6 of their papers we have counts for
6 papers
A generalization of formulas for the discriminants of quasi-orthogonal polynomials with applications to hypergeometric polynomials
Hideki Matsumura
Let be a field. In this article, we derive a formula for the discriminant of a sequence of polynomials. Here, and is a sequen…
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…
Quadrature formulas for Bessel polynomials
Hideki Matsumura
A quadrature formula is a formula computing a definite integration by evaluation at finite points. The existence of certain quadrature formulas for orthogonal polynomials is relate…
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…
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 with exactly two rational points. In the proof, we first show that the Mordell-Weil r…
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…