6 citations · 24 across the 19 of their papers we have counts for
20 papers
Exponential sums over singular binary quintics
Yasuhiro Ishitsuka
We give a characteristic-free explicit formula for exponential sums over singular binary quintic forms, based on the Waring decomposition of binary forms. This extends the method u…
Exponential sums over singular binary quartic forms and applications
Yasuhiro Ishitsuka, Takashi Taniguchi, Frank Thorne +1
We investigate exponential sums over singular binary quartic forms, proving an explicit formula for the finite field Fourier transform of this set. Our formula shares much in commo…
Periods modulo of integer sequences associated with division polynomials of genus curves
Yasuhiro Ishitsuka, Tetsushi Ito, Tatsuya Ohshita +2
We study an integer sequence associated with Cantor's division polynomials of a genus 2 curve having an integral point. We show that the reduction modulo of such a sequence is…
On the proportions of soluble forms in some families of locally soluble binary quartic forms
Yasuhiro Ishitsuka, Yoshinori Kanamura
An integral binary quartic form is said to be locally soluble (resp. soluble) if the corresponding genus one curve has a rational point over for every place of $…
The modularity of elliptic curves over all but finitely many totally real fields of degree 5
Yasuhiro Ishitsuka, Tetsushi Ito, Sho Yoshikawa
We study the finiteness of low degree points on certain modular curves and their Atkin--Lehner quotients, and, as an application, prove the modularity of elliptic curves over all b…
The arithmetic of a twist of the Fermat quartic
Yasuhiro Ishitsuka, Tetsushi Ito, Tatsuya Ohshita
We study the arithmetic of the twist of the Fermat quartic defined by which has no -rational point. We calculate the Mordell--Weil group of the Ja…
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…
The Hasse principle for finite Galois modules allowing exceptional sets of positive density
Yasuhiro Ishitsuka, Tetsushi Ito
We study a variant of the Hasse principle for finite Galois modules, allowing exceptional sets of positive density. For a Galois module whose underlying abelian group is isomorphic…
On algorithms to obtain linear determinantal representations of smooth plane curves of higher degree
Yasuhiro Ishitsuka, Tetsushi Ito, Tatsuya Ohshita
We give two algorithms to compute linear determinantal representations of smooth plane curves of any degree over any field. As particular examples, we explicitly give representativ…
Explicit calculation of the mod 4 Galois representation associated with the Fermat quartic
Yasuhiro Ishitsuka, Tetsushi Ito, Tatsuya Ohshita
We use explicit methods to study the 4-torsion points on the Jacobian variety of the Fermat quartic. With the aid of computer algebra systems, we explicitly give a basis of the gro…
An algorithm to obtain linear determinantal representations of smooth plane cubics over finite fields
Yasuhiro Ishitsuka
We give a brief report on our computations of linear determinantal representations of smooth plane cubics over finite fields. After recalling a classical interpretation of linear d…
Linear determinantal representations of smooth plane cubics over finite fields
Yasuhiro Ishitsuka
In this note, we study linear determinantal representations of smooth plane cubics over finite fields. We give an explicit formula of linear determinantal representations correspon…
A positive proportion of cubic curves over Q admit linear determinantal representations
Yasuhiro Ishitsuka
Can a smooth plane cubic be defined by the determinant of a square matrix with entries in linear forms in three variables? If we can, we say that it admits a linear determinantal r…
Sheaf theoretic classifications of pairs of square matrices over arbitrary fields
Yasuhiro Ishitsuka, Tetsushi Ito
We give classifications of linear orbits of pairs of square matrices with non-vanishing discriminant polynomials over a field in terms of certain coherent sheaves with additional d…
Orbit parametrizations of theta characteristics on hypersurfaces over arbitrary fields
Yasuhiro Ishitsuka
It is well-known that theta characteristics on smooth plane curves over a field of characteristic different from two are in bijection with certain smooth complete intersections of…
On the symmetric determinantal representations of the Fermat curves of prime degree
Yasuhiro Ishitsuka, Tetsushi Ito
We prove that the defining equations of the Fermat curves of prime degree cannot be written as the determinant of symmetric matrices with entries in linear forms in three variables…
The local-global principle for symmetric determinantal representations of smooth plane curves in characteristic two
Yasuhiro Ishitsuka, Tetsushi Ito
We give an application of Mumford's theory of canonical theta characteristics to a Diophantine problem in characteristic two. We prove that a smooth plane curve over a global field…
The local-global principle for symmetric determinantal representations of smooth plane curves
Yasuhiro Ishitsuka, Tetsushi Ito
A smooth plane curve is said to admit a symmetric determinantal representation if it can be defined by the determinant of a symmetric matrix with entries in linear forms in three v…
Complete Intersections of Two Quadrics and Galois Cohomology
Yasuhiro Ishitsuka
For each nonsingular hyperelliptic curve of arbitrary genus, we construct a natural injection from the Galois cohomology of 2-torsion subgroups of Jacobian varieties of the curve t…
On the ACC for lengths of extremal rays
Osamu Fujino, Yasuhiro Ishitsuka
We discuss the ascending chain condition for lengths of extremal rays. We prove that the lengths of extremal rays of -dimensional -factorial toric Fano varieties with…