5 papers
On a group of normalized solutions of the higher-dimensional Prouhet--Tarry--Escott problem
Munenori Inagaki, Hideki Matsumura, Masanori Sawa +1
We elucidate, for the first time, a novel group-theoretic structure that arises from certain solutions of the -dimensional Prouhet--Tarry--Escott problem of degree and size…
Geometric designs and Hilbert-Kamke equations of degree five for classical orthogonal polynomials
Teruyuki Mishima, Xiao-Nan Lu, Masanori Sawa +1
In this paper we elucidate the advantage of examining the connections between Hilbert-Kamke equations and geometric designs, or Chebyshev-type quadrature, for classical orthogonal…
The local-global property for bitangents of plane quartics
Yasuhiro Ishitsuka, Tetsushi Ito, Tatsuya Ohshita +2
We study the arithmetic of bitangents of smooth quartics over global fields. With the aid of computer algebra systems and using Elsenhans--Jahnel's results on the inverse Galois pr…
A remark on a Nagell-Lutz type statement for the Jacobian of a curve of genus 2 and a (2, 3, 6) quasi-torus decomposition of a sextic with 9 cusps
Hiro-o Tokunaga, Yukihiro Uchida
In this note, an analogous statement to the Nagell-Lutz theorem does not hold for the Jacobian of a certain curve of genus 2 over . As a by-product, we give a (2, 3,…
Discriminants of classical quasi-orthogonal polynomials, with combinatorial and number-theoretic applications
Masanori Sawa, Yukihiro Uchida
We derive explicit formulas for the resultants and discriminants of classical quasi-orthogonal polynomials, as a full generalization of the results of Dilcher and Stolarsky (2005)…