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Number Theory Seminar
Seminar information archive ～06/13｜Next seminar｜Future seminars 06/14～
| Date, time & place | Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Naoki Imai, Shane Kelly |
2021/07/07
17:00-18:00 Online
Takumi Yoshida (Keio University)
On the BSD conjecture for the quadratic twists of the elliptic curve $X_0(49)$ (Japanese)
Takumi Yoshida (Keio University)
On the BSD conjecture for the quadratic twists of the elliptic curve $X_0(49)$ (Japanese)
[ Abstract ]
The full BSD conjecture (the full Birch-Swinnerton-Dyer conjecture) is the important conjecture, which connects the algebraic invariants and analytic invariants of elliptic curves. When the elliptic curve is defined over $\mathbb{Q}$, these invariants are known to be rational numbers. Now, even when the elliptic curve is defined over $\mathbb{Q}$ and the $L$-function is not $0$ at $s=1$, it is not shown that the $2$-orders of these invariants are equal. Coates, Kim, Liang and Zhao proved the full BSD conjecture for some quadratic twists of $X_0(49)$, by proving that these $2$-orders are same. We extends this result, and prove the full BSD conjecture for more twists.
The full BSD conjecture (the full Birch-Swinnerton-Dyer conjecture) is the important conjecture, which connects the algebraic invariants and analytic invariants of elliptic curves. When the elliptic curve is defined over $\mathbb{Q}$, these invariants are known to be rational numbers. Now, even when the elliptic curve is defined over $\mathbb{Q}$ and the $L$-function is not $0$ at $s=1$, it is not shown that the $2$-orders of these invariants are equal. Coates, Kim, Liang and Zhao proved the full BSD conjecture for some quadratic twists of $X_0(49)$, by proving that these $2$-orders are same. We extends this result, and prove the full BSD conjecture for more twists.
