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Number Theory Seminar
Seminar information archive ～05/22｜Next seminar｜Future seminars 05/23～
| Date, time & place | Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Naoki Imai, Shane Kelly |
2008/11/26
16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
平田典子 (日本大学理工学部)
Lang's Observation in Diophantine Problems
平田典子 (日本大学理工学部)
Lang's Observation in Diophantine Problems
[ Abstract ]
In 1964, Serge Lang suggested the following problem, which reads now as follows:
Let E be an elliptic curve defined over a number field K, and varphi be a rational function on E. Then, for every point PinE(K) where varphi does not vanish at P, the logarithms of a norm of varphi(P) is at worst linear in the logarithms of the Neron-Tate height of the point P.
We give a simultaneous Diophantine approximation for linear forms in elliptic logarithms which actually implies this conjecture. We also present Lang's observations in Diophantine problems.
In 1964, Serge Lang suggested the following problem, which reads now as follows:
Let E be an elliptic curve defined over a number field K, and varphi be a rational function on E. Then, for every point PinE(K) where varphi does not vanish at P, the logarithms of a norm of varphi(P) is at worst linear in the logarithms of the Neron-Tate height of the point P.
We give a simultaneous Diophantine approximation for linear forms in elliptic logarithms which actually implies this conjecture. We also present Lang's observations in Diophantine problems.
