Alladi Ramakrishnan Hall

Eisenstein elements inside the space of modular symbols

Debargha Banerjee

IISER Pune

The Eisenstein elements inside the space of modular symbols
are the explicit elements of the space of modular symbols corresponding
to Eisenstein series of weight two. In the talk, we will show how to write down an explicit rational
expression of Eisenstein elements in terms of Manin symbols, giving an answer
to a question of Loic Merel.
We also compute the winding elements explicitly
for some congruence subgroups. Our results are explicit versions of the Manin-Drinfeld Theorem.
A part of these work is joint with Srilakshmi Krishnamoorthy (IIT, M).