Algebraic independence of periods and logarithms of Drinfeld modules (with an appendix by Brian Conrad)
By Chieh-Yu Chang, Matthew A. Papanikolas. 2010
47 citations recorded by the source corpus.
Let rho be a Drinfeld A-module with generic characteristic defined over an algebraic function field. We prove that all of the algebraic relations among periods, quasi-periods, and logarithms of algebraic points on rho are those coming from linear relations induced by endomorphisms of rho.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/fbb845b6d355be7b93766a0eb9516df3196b603f
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In Algebra and Number Theory
In Geometry and Topology
Citations in the corpus
- Linear independence of monomials of multizeta values in positive characteristic (2012, background): “ as a function field analogue of Grothendieck’s periods conjecture. Using these tools, one has the algebraic independence results on Carlitz zeta values [CY07], Drinfeld logarithms at algebraic points [CP12] etc. Although one is able to construct suitable t-motives so that the given multizeta values ”
- Special L-values of Drinfeld modules (2010, background): “overs the formula ζ(k[t],1)=exp−1(1) that was already known to Carlitz [6, p. 160] [3, p.199]. 5 Remark 4. The quantity [R : exp− 1 E E(R)]∈k((T−))is typicallytranscendental over k(T), see [14], [8], [7]. Remark5. Althoughwewillnotneedthis, webrieflyindicatehow L(E/R) is the value at some integer s o”