S. Yamagishi

activity

20112023

most citedArithmetic of higher-dimensional orbifolds and a mixed Waring problem

6 citations · 24 across the 18 of their papers we have counts for

collaborators

18 papers

math.NT2023

Quartic polynomials in two variables do not represent all non-negative integers

Stanley Yao Xiao, Shuntaro Yamagishi

In this paper, we prove that there does not exist $F \in Q [x, y]$ of degree $4$ such that $F (Z^{2}) = Z_{\geq 0}$ . In particular, this answers a question by…

math.NT2023★ 2 cited

Birch's theorem on forms in many variables with a Hessian condition

Shuntaro Yamagishi

Let $F \in Z [x_{1}, \dots, x_{n}]$ be a homogeneous form of degree $d \geq 2$ , and $V_{F}^{*}$ the singular locus of the hypersurface $\{\mathbf{x} \in \mathbb{A}^n_{\mathbb{C}}:…

math.NT2022

Density of rational points on manifolds and Diophantine approximation on hypersurfaces

Shuntaro Yamagishi

In this article, we establish an analogue of the dimension growth conjecture, which is regarding the density of rational points on projective varieties, for compact submanifolds of…

math.NT2021★ 1 cited

Diophantine equations in primes: density of prime points on affine hypersurfaces II

Shuntaro Yamagishi

Let $F \in Z [x_{1}, \dots, x_{n}]$ be a homogeneous form of degree $d \geq 2$ , and let $V_{F}^{*}$ denote the singular locus of the affine variety $V(F) = \{ \mathbf{z} \in {\mat…

math.NT2021

Diophantine equations in primes: density of prime points on affine hypersurfaces

Shuntaro Yamagishi

Let $F \in Z [x_{1}, \dots, x_{n}]$ be a homogeneous form of degree $d \geq 2$ , and let $V_{F}^{*}$ denote the singular locus of the affine variety $V(F) = \{ \mathbf{z} \in {\mat…

math.NT2021★ 3 cited

Density of rational points near/on compact manifolds with certain curvature conditions

D. Schindler, S. Yamagishi

In this article we establish an asymptotic formula for the number of rational points, with bounded denominators, within a given distance to a compact submanifold $M$ of $…

math.NT2019★ 6 cited

Arithmetic of higher-dimensional orbifolds and a mixed Waring problem

Tim Browning, Shuntaro Yamagishi

We study the density of rational points on a higher-dimensional orbifold $(P^{n - 1}, D)$ when $D$ is a $Q$ -divisor involving hyperplanes. This allows us to address…

math.NT2018

On an oscillatory integral involving a homogeneous form

Shuntaro Yamagishi

Let $F \in R [x_{1}, \dots, x_{n}]$ be a homogeneous form of degree $d > 1$ satisfying $(n - dim V_{F}^{*}) > 4$ , where $V_{F}^{*}$ is the singular locus of $V(F) = \{ \mathbf{z} \…

math.NT2017★ 4 cited

Diophantine equations in semiprimes

Shuntaro Yamagishi

A semiprime is a natural number which is the product of two (not necessarily distinct) prime numbers. Let $F (x_{1}, \dots, x_{n})$ be a degree $d$ homogeneous form with integer coeffi…

math.NT2017★ 4 cited

Prime solutions to polynomial equations in many variables and differing degrees

Shuntaro Yamagishi

Let $f = (f_{1}, \dots, f_{R})$ be a system of polynomials with integer coefficients in which the degrees need not all be the same. We provide sufficient conditions for which…

math.NT2016★ 1 cited

Exponential sum estimate for systems including linear polynomials

Shuntaro Yamagishi

In his paper, W. M. Schmidt obtained an exponential sum estimate for systems of polynomials not including linear polynomials, which was then used to apply the Hardy-Littlewood circ…

math.NT2015★ 2 cited

Zeroes of polynomials with prime inputs and Schmidt's $h$ -invariant

Stanley Yao Xiao, Shuntaro Yamagishi

In this paper we show that a polynomial equation admits infinitely many prime-tuple solutions assuming only that the equation satisfies suitable local conditions and the polynomial…

math.NT2015

Sidon basis in polynomial rings over finite fields

Wentang Kuo, Shuntaro Yamagishi

Let $F_{q} [t]$ denote the ring of polynomials over $F_{q}$ , the finite field of $q$ elements. Suppose the characteristic of $F_{q}$ is not $2$ or $3$ . In this…

math.NT2015

On a problem of Sidon for polynomials over finite fields

Wentang Kuo, Shuntaro Yamagishi

Let $ω$ be a sequence of positive integers. Given a positive integer $n$ , we define $r_{n} (ω) = ∣ {(a, b) \in N \times N : a, b \in ω, a + b = n, 0 < a < b} ∣.$ S…

math.NT2015

Diophantine approximation of polynomials over $F_{q} [t]$ satisfying a divisibility condition

Shuntaro Yamagishi

Let $F_{q} [t]$ denote the ring of polynomials over $F_{q}$ , the finite field of $q$ elements. We prove an estimate for fractional parts of polynomials over $\mathbb{F…

math.NT2015

The asymptotic formula for Waring's problem in function fields

Shuntaro Yamagishi

Let $F_{q} [t]$ be the ring of polynomials over $F_{q}$ , the finite field of $q$ elements, and let $p$ be the characteristic of $F_{q}$ . We denote $\widetilde{G…

math.NT2014

A generalization of a theorem of Erdős-Rényi to $m$ -fold sums and differences

Kathryn Hare, Shuntaro Yamagishi

Let $m \geq 2$ be a positive integer. Given a set $E (ω) \subseteq N$ we define $r_{N}^{(m)} (ω)$ to be the number of ways to represent $N \in Z$ as any combination of…

math.NT2011★ 1 cited

Computing the moment polynomials of the zeta function

Michael O. Rubinstein, Shuntaro Yamagishi

We describe a method to accelerate the numerical computation of the coefficients of the polynomials $P_{k} (x)$ that appear in the conjectured asymptotics of the $2 k$ -th moment of the…

Quartic polynomials in two variables do not represent all non-negative integers

Birch's theorem on forms in many variables with a Hessian condition

Density of rational points on manifolds and Diophantine approximation on hypersurfaces

Diophantine equations in primes: density of prime points on affine hypersurfaces II

Diophantine equations in primes: density of prime points on affine hypersurfaces

Density of rational points near/on compact manifolds with certain curvature conditions

Arithmetic of higher-dimensional orbifolds and a mixed Waring problem

On an oscillatory integral involving a homogeneous form

Diophantine equations in semiprimes

Prime solutions to polynomial equations in many variables and differing degrees

Exponential sum estimate for systems including linear polynomials

Zeroes of polynomials with prime inputs and Schmidt's h-invariant

Sidon basis in polynomial rings over finite fields

On a problem of Sidon for polynomials over finite fields

Diophantine approximation of polynomials over Fq​[t] satisfying a divisibility condition

The asymptotic formula for Waring's problem in function fields

A generalization of a theorem of Erdős-Rényi to m-fold sums and differences

Computing the moment polynomials of the zeta function

Zeroes of polynomials with prime inputs and Schmidt's $h$ -invariant

Diophantine approximation of polynomials over $F_{q} [t]$ satisfying a divisibility condition

A generalization of a theorem of Erdős-Rényi to $m$ -fold sums and differences