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Semiabelian varieties and transcendence on Weierstrass sigma functions

Part of: Algebraic number theory: local and $p$-adic fields Diophantine approximation, transcendental number theory Abelian varieties and schemes

Published online by Cambridge University Press:  25 November 2024

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
*
Email: phamduchiep@vnu.edu.vn
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Abstract

We establish new results on complex and $p$-adic linear independence on a class of semiabelian varieties. As applications, we obtain transcendence results concerning complex and $p$-adic Weierstrass sigma functions associated with elliptic curves.

Keywords

p-adicsemiabelian varietiestranscendenceWeierstrass sigma functions

MSC classification

Primary: 11J95: Results involving abelian varieties
Secondary: 11J72: Irrationality; linear independence over a field 11S99: None of the above, but in this section 14K12: Subvarieties
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 67 , Issue 1 , January 2025 , pp. 107 - 113
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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Footnotes

Dedicated to my Father-in-law, Dr. Ngoc Quang Le on the occasion of his 65th birthday.

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