| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Research Abstract |
We prove a new Diophantine approximation for linear forms in elliptic logarithms (in Crelle, vol.628, with S.David). As far as the height of the linear forms is concerned, our result is the first optimal one. We thus solve a conjecture of S.Lang dating back to 1964. We also show a p-adic version in a case, namely, a lower bound for linear forms in two p-adic elliptic logarithms. We refine here previous estimates in the dependency on the height of algebraic coefficients of the linear forms (the p-adic result is in press in Kyushu Journal of Mathematics, vol.64, No.2, 2010). A lower bound for linear form, in n terms of p-adic elliptic logarithms, is in preparation. This generalization would be useful to determine the set of S-integer points on elliptic curves defined over a number field, whenever we know a basis of the Mordell-Weil group.
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