S. Fukuhara

activity

20042017

most citedGeneralized Kronecker formula for Bernoulli numbers and self-intersections of curves on a surface

1 citations · 2 across the 8 of their papers we have counts for

collaborators

8 papers

math.GT2017

Kauffman-Jones polynomial of a curve on a surface

Shinji Fukuhara, Yusuke Kuno

We introduce a Kauffman-Jones type polynomial $L_{γ} (A)$ for a curve $γ$ on an oriented surface, whose endpoints are on the boundary of the surface. The polynomial $\mathca…

math.NT2015★ 1 cited

Generalized Kronecker formula for Bernoulli numbers and self-intersections of curves on a surface

Shinji Fukuhara, Nariya Kawazumi, Yusuke Kuno

We present a new explicit formula for the $m$ -th Bernoulli number $B_{m}$ , which involves two integer parameters $a$ and $n$ with $0 \leq a \leq m \leq n$ . If we set $a = 0$ and $n = m$ , then…

math.NT2010

A new basis for the space of modular forms

Shinji Fukuhara

Let $G_{2 n}$ be the Eisenstein series of weight $2 n$ for the full modular group $Γ=SL_2(\ZZ)$. It is well-known that the space $M_{2 k}$ of modular forms of weight $2 k$ on $Γ$ has a…

math.NT2009

The elliptic Apostol-Dedekind sums generate odd Dedekind symbols with Laurent polynomial reciprocity laws

Shinji Fukuhara

Dedekind symbols are generalizations of the classical Dedekind sums (symbols). There is a natural isomorphism between the space of Dedekind symbols with Laurent polynomial reciproc…

math.NT2009

Twisted Hecke L-values and period polynomials

Shinji Fukuhara, Yifan Yang

Let $f_{1}, ..., f_{d}$ be an orthogonal basis for the space of cusp forms of even weight $2 k$ on $Γ_{0} (N)$ . Let $L (f_{i}, s)$ and $L (f_{i}, χ, s)$ denote the $L$ -function of $f_{i}$ and its twist…

math.NT2006

Period polynomials and explicit formulas for Hecke operators on Γ_0(2)

Shinji Fukuhara, Yifan Yang

Let S_{w+2}(Γ_0(N)) be the vector space of cusp forms of weight w+2 on the congruence subgroup Γ_0(N). We first determine explicit formulas for period polynomials of elements in S_…