WEIERSTRASS ZETA FUNCTIONS AND p -ADIC LINEAR RELATIONS.

PHAM, DUC HIEP

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].

ELLIPTIC functions; ALGEBRAIC numbers; ALGEBRAIC fields; GEOMETRY; MATHEMATICS

Bulletin of the Australian Mathematical Society, 2024, Vol 110, Issue 2, p234

0004-9727

Academic Journal

10.1017/S0004972724000091