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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

DUC HIEP PHAM Open the ORCID record for DUC HIEP PHAM [Opens in a new window]
DUC HIEP PHAM*
Affiliation:
University of Education, Vietnam National University, Hanoi, 144 Xuan Thuy, Cau Giay, Hanoi, Vietnam
*
e-mail: phamduchiep@vnu.edu.vn
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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.

Keywords

elliptic curveelliptic functionp-adic transcendence

MSC classification

Primary: 11J89: Transcendence theory of elliptic and abelian functions
Secondary: 11G07: Elliptic curves over local fields 11S99: None of the above, but in this section
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 105 , Issue 1 , February 2022 , pp. 31 - 36
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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