arXiv subjects

Yusuke Fujiyoshi

Publications and source records attributed to Yusuke Fujiyoshi.

2 recordsLinked to original sources

arXiv2026

On the finiteness of prime trees and their relation to modular forms

In this paper, we introduce the prime trees associated with a finite subset $P$ of the set of all prime numbers, and provide conditions under which the tree is of finite type. Moreover, we compute the density of finite-type subsets $P$. As an application, we show that for weight $k \ge 2$ and levels $N = N'\prod_{p \in P} p^{a_p}$, where $N'$ is squarefree and $a_{p} \geq 2$, every cusp form $f \in \mathcal{S}_k(\Gamma_0(N))$ can be expressed as a linear combination of products of two specific Eisenstein series whenever $P$ is of finite type.

math.NT↗

arXiv2025

Cyclic-quasi-injective for Finite Abelian Groups

We investigate the conditions for a finite abelian group $G$ under which any cyclic subgroup $H$ and any group homomorphism $f \in \operatorname{Hom}(H,G)$ can be extended to an endomorphism $F \in \operatorname{End}(G)$. As a result, we provide necessary and sufficient conditions for such a group $G$ and we compute the number of cyclic subgroups possessing non-extendable homomorphisms. In addition, we demonstrate that the number of cyclic subgroups that do not satisfy the conditions corresponds to the sum of the maximum jumps in the associated permutations given by $\sum_{\sigma \in S_{n}} \max_{1 \leq i \leq n} \{\sigma(i) - i\}$.

math.GR↗