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Number Theory Seminar
Seminar information archive ～06/25｜Next seminar｜Future seminars 06/26～
| 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 X0(49) (Japanese)
Takumi Yoshida (Keio University)
On the BSD conjecture for the quadratic twists of the elliptic curve X0(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 Q, these invariants are known to be rational numbers. Now, even when the elliptic curve is defined over 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 X0(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 Q, these invariants are known to be rational numbers. Now, even when the elliptic curve is defined over 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 X0(49), by proving that these 2-orders are same. We extends this result, and prove the full BSD conjecture for more twists.
