The least prime number represented by a binary quadratic form
Event details
| Date | 02.12.2019 |
| Hour | 15:45 › 16:45 |
| Speaker | Nasır Talebizadeh Sardari (Max-Planck-Institut für Matematik, Bonn) |
| Location | |
| Category | Conferences - Seminars |
Let $D<0$ be a fundamental discriminant and $h(D)$ be the class number of $\mathbb{Q}(\sqrt{D})$. Let $R(X,D)$ be the number of classes of the binary quadratic forms
of discriminant $D$ which represent a prime number in the interval $[X,2X]$. Moreover, assume that $\pi_{D}(X)$ is the number of primes, which split in $\mathbb{Q}(\sqrt{D})$ with norm in the interval $[X,2X].$ We prove that
$$\Big(\frac{\pi_D(X)}{\pi(X)}\Big)^2 \ll \frac{R(X,D)}{h(D)}\Big(1+\frac{h(D)}{\pi(X)}\Big),$$
where $\pi(X)$ is the number of primes in the interval $[X,2X]$ and the implicit constant in $\ll$ is independent of $D$ and $X$.
Practical information
- Informed public
- Free
Organizer
- Matthew de Courcy
Contact
- Monique Kiener