On Periods of the Third Kind for Rank 2 Drinfeld Modules
نویسنده
چکیده
In analogy with the periods of abelian integrals of differentials of the third kind for an elliptic curve defined over a number field, we introduce a notion of periods of the third kind for a rank 2 Drinfeld Fq[t]-module ρ defined over an algebraic function field. In this paper we establish explicit formulae for these periods of the third kind for ρ. Combining with the main result in [Chang-Papanikolas 2012], we show the algebraic independence of the periods of first, second and third kinds for ρ.
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Periods of Third Kind for Rank 2 Drinfeld Modules and Algebraic Independence of Logarithms
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 ρ defined over an algebraic function field and derive explicit formulae for them. When ρ has complex multiplication by a separable extension, we prove the algebraic independence of ρlo...
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