#### 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).

Done