Irreducibility of the zero polynomials of Eisenstein series

Let E k be the normalized Eisenstein series of weight k on SL 2 ( Z ) . Let φ k be the polynomial that encodes the j -invariants of non-elliptic zeros of E k . In 2001, Gekeler observed that the polynomials φ k seem to be irreducible (and verified this claim for k ≤ 446 ). We show that φ k is irredu...

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Bibliographic Details
Published in:Archiv der Mathematik 2022, Vol.119 (4), p.351-358
Main Author: González, Oscar E.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Polynomials
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Summary:Let E k be the normalized Eisenstein series of weight k on SL 2 ( Z ) . Let φ k be the polynomial that encodes the j -invariants of non-elliptic zeros of E k . In 2001, Gekeler observed that the polynomials φ k seem to be irreducible (and verified this claim for k ≤ 446 ). We show that φ k is irreducible for infinitely many k .
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-022-01766-6