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WEIERSTRASS ZETA FUNCTIONS AND p-ADIC LINEAR RELATIONS
Published online by Cambridge University Press: 11 March 2024
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].
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- Research Article
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- © The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
Footnotes
This research has been done under the research project QG.23.48 ‘Some selected topics in number theory’ of Vietnam National University, Hanoi.