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ELLIPTIC CURVES AND $\boldsymbol {p}$-ADIC ELLIPTIC TRANSCENDENCE
Part of:
Arithmetic algebraic geometry
Algebraic number theory: local and $p$-adic fields
Diophantine approximation, transcendental number theory
Published online by Cambridge University Press: 21 May 2021
Abstract
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.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 105 , Issue 1 , February 2022 , pp. 31 - 36
- Copyright
- © 2021 Australian Mathematical Publishing Association Inc.
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