S. Yamagishi

activity

20162023

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

6 citations · 16 across the 8 of their papers we have counts for

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11 papers · 1 filter

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

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 $…