Algebraic Independence of Values of Elliptic Functions
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Interpolation Formulas and Auxiliary Functions
We prove an interpolation formula for ``semi-cartesian products'' and use it to study several constructions of auxiliary functions. We get in this way a criterion for the values of the exponential map of an elliptic curve E defined over Q. It reduces the analogue of Schanuel's conjecture for the elliptic logarithms of E to a statement of the form of a criterion of algebraic independence. We als...
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For any rank 2 Drinfeld module ρ defined over an algebraic function field, we consider its period matrix Pρ, which is analogous to the period matrix of an elliptic curve defined over a number field. Suppose that the characteristic of the finite field Fq is odd and that ρ does not have complex multiplication. We show that the transcendence degree of the field generated by the entries of Pρ over ...
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