arXiv subjects
Publications and source records attributed to Yoshikatsu Yashiro.
Let $F(s)$ be a function belonging to Selberg class. Chandrasekharan and Narasiman proved the approximate functional equation for $F(s)$. In this paper, we shall generalize this formula for the derivatives of $F(s)$.
Let $f$ be a holomorphic cusp form of weight $k$ with respect to full modular group $SL_2(\mathbb{Z})$ satisfying a normalized Hecke eigenform, $L_f(s)$ the $L$-function attached to the form $f$. Good gave the approximate functional equation and mean square formula of $L_f(s)$. In this paper, we shall generalize these formulas for the derivatives of $L_f(s)$.
In 1874, Mertens proved the approximate formula for partial Euler product for Riemann zeta function at $s=1$, which is called Mertens' theorem. In this paper, we generalize Mertens' theorem for Selberg class and show the prime number theorem for Selberg class.
Let $f$ be a holomorphic cusp form of weight $k$ with respect to $SL_2(\mathbb{Z})$ which is a normalized Hecke eigenform, $L_f(s)$ the $L$-function attached to the form $f$. In this paper, we shall give the relation of the number of zeros of $L_f(s)$ and the derivatives of $L_f(s)$ using Berndt's method, and an estimate of zero-density of the derivatives of $L_f(s)$ based on Littlewood's method.
Let $S_k$ be the space of holomorphic cusp forms of weight $k$ with respect to $SL_2(\mathbb{Z})$. Let $f \in S_k$ be a normalized Hecke eigenform, $L_f(s)$ the $L$-function attached to the form $f$. In this paper we consider the distribution of zeros of $L_f(s)$ in the strip $σ\leq \Re s \leq 1$ for fixed $σ>1/2$ with respect to the imaginary part. We study estimates of \[ N_f(σ,T) = #\{ρ\in\mathbb{C} \mid L_f(ρ)=0, σ leq \Reρ\leq 1, 0 \leq \Imρ\leq T} \] for $1/2 \leq σ\leq1$ and large $T>0$. Using the methods of Karatsuba and Voronin we shall give another proof for Ivić's method.