Yusuke Nemoto

collaborators

6 papers

math.NT2026

Elements in $K_{4}$ and regulator maps of Fermat curves

FranÃ§ois Brunault, David T. -B. G. Lilienfeldt, Yusuke Nemoto

We construct explicit elements in the group $K_{4}^{(3)}$ of the Fermat curves $x^{N} + y^{N} = 1$ for all $N \geq 3$ . The construction, which is uniform in $N$ , uses polylogarithmic complexe…

math.AG2026

Construction of higher Chow cycles on cyclic coverings of $P^{1} \times P^{1}$ , Part II

Yusuke Nemoto, Ken Sato

In this paper, we construct higher Chow cycles of type $(2, 1)$ on a family of surfaces related to a product of curves, which are certain degree $N$ abelian covers of $\mathbb{P}^1…

math.NT2026

Mixed motives and linear forms in the Catalan constant

Payman Eskandari, Kumar Murty, Yusuke Nemoto

We first give a geometric construction of a 2-dimensional mixed motive over $Q$ with the Catalan constant $G = 1 - 1/ 3^{2} + 1/ 5^{2} - 1/ 7^{2} + \dots$ as a period. We then use…

math.AG2026

The modified diagonal cycles of Hypergeometric curves

Payman Eskandari, Yusuke Nemoto

For each $N \geq 2$ , Asakura and Otsubo have recently introduced a smooth family of algebraic curves ${X_{N, I^»}}_{I^» \in P^{1} ∖ {0, 1, \infty}}$ in characteristic…

math.NT2025

Regulators on some abelian coverings of $P^{1}$ minus $n + 2$ points

Yusuke Nemoto, Takuya Yamauchi

In this paper, we construct certain rational or integral elements in the motivic cohomology of superelliptic curves which are quotient curves of abelian coverings of $P^{1}$ …

math.AG2025

Construction of Higher Chow cycles on cyclic coverings of $P^{1} \times P^{1}$

Yusuke Nemoto, Ken Sato

In this paper, we construct higher Chow cycles of type $(2, 1)$ on a certain family of surfaces, which are constructed by a product of certain hypergeometric curves of degree $N$ .…

Elements in K4​ and regulator maps of Fermat curves

Construction of higher Chow cycles on cyclic coverings of P1×P1, Part II