Please use this identifier to cite or link to this item: http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/8358
Title: Eisenstein cycles and Manin-Drinfeld properties
Authors: BANERJEE, DEBARGHA
Merel, Loic
Dept. of Mathematics
Keywords: Eisenstein series
Modular symbols
special values of L-functions
2023-DEC-WEEK3
TOC-DEC-2023
2024
Issue Date: Nov-2023
Publisher: Walter De Gruyter
Citation: Forum Mathematicum, 36(02).
Abstract: Let Gamma be a subgroup of finite index of SL2(Z). We give an analytic criterion for a cuspidal divisor to be torsion in the Jacobian J(Gamma) of the corresponding modular curve X-Gamma. Our main tool is the explicit description, in terms of modular symbols, of what we call Eisenstein cycles. The latter are representations of relative homology classes over which integration of any holomorphic differential forms vanishes. Our approach relies in an essential way on the specific case Gamma subset of Gamma(2), where we can consider convenient generalized Jacobians instead of J(Gamma). We relate the Eisenstein classes to the scattering constants attached to Eisenstein series. Finally, we illustrate our approach by considering Fermat curves.
URI: https://doi.org/10.1515/forum-2022-0116
http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/8358
ISSN: 0933-7741
1435-5337
Appears in Collections:JOURNAL ARTICLES

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