Keiichiro Nomoto

activity

20212024

collaborators

3 papers

math.NT2024

The 2-adic valuations of the algebraic central $L$ -values for quadratic twists of weight 2 newforms

Taiga Adachi, Keiichiro Nomoto, Ryota Shii

Let $f$ be a normalized newform of weight 2 on $Γ_{0} (N)$ whose coefficients lie in $Q$ and let $χ_{M}$ be a primitive quadratic Dirichlet character with conductor $M$ . In thi…

math.NT2022

Lower bound for the 2-adic valuations of central $L$ -values of elliptic curves with complex multiplication

Keiichiro Nomoto

Let $E_{- D}$ be the elliptic curve $y^{2} = x^{3} + D x$ defined over $K = Q (i)$ for $D \in K$ which is coprime to 2. In this paper, we give a lower bound for the 2-adic valuation of…

math.NT2021

The rank of a CM elliptic curve and a recurrence formula

Keiichiro Nomoto

Let $p$ be a prime number and $E_{p}$ denote the elliptic curve $y^{2} = x^{3} + p x$ . It is known that for $p$ which is congruent to $1, 9$ modulo $16$ , the rank of $E_{p}$ over $\mathbb{Q…

The 2-adic valuations of the algebraic central L-values for quadratic twists of weight 2 newforms

Lower bound for the 2-adic valuations of central L-values of elliptic curves with complex multiplication

The rank of a CM elliptic curve and a recurrence formula

The 2-adic valuations of the algebraic central $L$ -values for quadratic twists of weight 2 newforms

Lower bound for the 2-adic valuations of central $L$ -values of elliptic curves with complex multiplication