The finiteness of derivation-invariant prime ideals and the algebraic independence of the Eisenstein series

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We prove that for a graded algebra A with a derivation D-A satisfying certain conditions, and a bi-graded algebra A[q] with an extended derivation D of D-A, there are only finitely many D-A- and D-invariant (or differential with respect to D-A and D) principal prime ideals of A and of A[q], respectively. As its application, we prove the algebraic independence of the values of certain Eisenstein series for the arithmetic Hecke groups H(m) for m = 4, 6, infinity, which is an extension of Nesterenko's result for the Eisenstein series for SL2(Z).
Publisher
SPRINGER
Issue Date
2021-12
Language
English
Article Type
Article
Citation

RAMANUJAN JOURNAL, v.56, no.3, pp.865 - 889

ISSN
1382-4090
DOI
10.1007/s11139-021-00404-z
URI
http://hdl.handle.net/10203/289462
Appears in Collection
MA-Journal Papers(저널논문)
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