Periods of third kind for rank 2 Drinfeld modules and algebraic independence of logarithms
arXiv:0909.0101
Abstract
In analogy with the periods of abelian integrals of differentials of third kind for an elliptic curve defined over a number field, we introduce a notion of periods of third kind for a rank 2 Drinfeld Fq[t]-module rho defined over an algebraic function field and derive explicit formulae for them. When rho has complex multiplication by a separable extension, we prove the algebraic independence of rho-logarithms of algebraic points that are linearly independent over the CM field of rho. Together with the main result in [CP08], we completely determine all the algebraic relations among the periods of first, second and third kinds for rank 2 Drinfeld Fq[t]-modules in odd characteristic.
arXiv comment19 pages
References in corpus (5)
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