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ELLIPTIC CURVES AND -ADIC ELLIPTIC TRANSCENDENCE
Bulletin of the Australian Mathematical Society ( IF 0.6 ) Pub Date : 2021-05-21 , DOI: 10.1017/s0004972721000320 DUC HIEP PHAM
Bulletin of the Australian Mathematical Society ( IF 0.6 ) Pub Date : 2021-05-21 , DOI: 10.1017/s0004972721000320 DUC HIEP PHAM
We prove a necessary and sufficient condition for isogenous elliptic curves based on the algebraic dependence of p -adic elliptic functions. As a consequence, we give a short proof of the p -adic analogue of Schneider’s theorem on the linear independence of p -adic elliptic logarithms of algebraic points on two nonisogenous elliptic curves defined over the field of algebraic numbers.
中文翻译:
椭圆曲线和-ADIC 椭圆超越
我们基于代数相关性证明了等生椭圆曲线的充要条件p -adic 椭圆函数。因此,我们给出一个简短的证明p - Schneider 定理关于线性独立性的进数类似物p -在代数数域上定义的两条非同质椭圆曲线上代数点的进数椭圆对数。
更新日期:2021-05-21
中文翻译:
椭圆曲线和-ADIC 椭圆超越
我们基于代数相关性证明了等生椭圆曲线的充要条件