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A note on the Eisenstein elements of prime square level


Author: Debargha Banerjee
Journal: Proc. Amer. Math. Soc. 142 (2014), 3675-3686
MSC (2010): Primary 11F67; Secondary 11F11, 11F20, 11F30
DOI: https://doi.org/10.1090/S0002-9939-2014-12097-1
Published electronically: July 3, 2014
MathSciNet review: 3251709
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Abstract: We explicitly write the Eisenstein elements inside the space of modular symbols corresponding to each Eisenstein series for the congruence subgroup $ \Gamma _0(p^2)$, answering a question of Merel. As a consequence, we also write the winding element explicitly for the congruence subgroup $ \Gamma _0(p^2)$.


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Additional Information

Debargha Banerjee
Affiliation: Mathematical Sciences Institute, Australian National University, Canberra ACT 0200, Australia
Address at time of publication: Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pashan, Pune 411 008, India
Email: debargha.banerjee@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2014-12097-1
Keywords: Eisenstein series, modular symbols, special values of $L$-functions
Received by editor(s): December 21, 2011
Received by editor(s) in revised form: October 11, 2012, and November 15, 2012
Published electronically: July 3, 2014
Additional Notes: The author was partially supported by the ARC grant DP0773301.
Communicated by: Lev Borisov
Article copyright: © Copyright 2014 American Mathematical Society