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WEIERSTRASS ZETA FUNCTIONS AND p-ADIC LINEAR RELATIONS

Published online by Cambridge University Press:  11 March 2024

DUC HIEP PHAM*
Affiliation:
University of Education, Vietnam National University, Hanoi, 144 Xuan Thuy, Cau Giay, Hanoi, Vietnam

Abstract

We discuss the p-adic Weierstrass zeta functions associated with elliptic curves defined over the field of algebraic numbers and linear relations for their values in the p-adic domain. These results are extensions of the p-adic analogues of results given by Wüstholz in the complex domain [see A. Baker and G. Wüstholz, Logarithmic Forms and Diophantine Geometry, New Mathematical Monographs, 9 (Cambridge University Press, Cambridge, 2007), Theorem 6.3] and also generalise a result of Bertrand to higher dimensions [‘Sous-groupes à un paramètre p-adique de variétés de groupe’, Invent. Math. 40(2) (1977), 171–193].

Type
Research Article
Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

This research has been done under the research project QG.23.48 ‘Some selected topics in number theory’ of Vietnam National University, Hanoi.

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