Reference : A Conjecture of Coleman on the Eisenstein Family
E-prints/Working papers : Already available on another site
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/51649
A Conjecture of Coleman on the Eisenstein Family
English
Advocaat, Bryan mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
Kiming, Ian []
Wiese, Gabor mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
2022
No
[en] We prove for primes $p\ge 5$ a conjecture of Coleman on the analytic continuation of the family of modular functions $\frac{\Es_\k}{V(\Es_\k)}$ derived from the family of Eisenstein series $\Es_\k$.

The precise, quantitative formulation of the conjecture involved a certain on $p$ depending constant. We show by an example that the conjecture with the constant that Coleman conjectured cannot hold in general for all primes. On the other hand, the constant that we give is also shown not to be optimal in all cases.

The conjecture is motivated by its connection to certain central statements in works by Buzzard and Kilford, and by Roe, concerning the ``halo'' conjecture for the primes $2$ and $3$, respectively. We show how our results generalize those statements and comment on possible future developments.
http://hdl.handle.net/10993/51649
https://arxiv.org/abs/2207.03822
FnR ; FNR12246620 > Hugo Parlier > GPS > Geometry, Probability And Their Synergies > 01/01/2019 > 30/06/2025 > 2017

File(s) associated to this reference

Fulltext file(s):

FileCommentaryVersionSizeAccess
Open access
eisenstein_family18.pdfAuthor preprint387.46 kBView/Open

Bookmark and Share SFX Query

All documents in ORBilu are protected by a user license.