Vol. 281, No. 2, 2016

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The Eisenstein elements of modular symbols for level product of two distinct odd primes

Debargha Banerjee and Srilakshmi Krishnamoorthy

Vol. 281 (2016), No. 2, 257–285
Abstract

We explicitly write down the Eisenstein elements inside the space of modular symbols for Eisenstein series with integer coefficients for the congruence subgroups ${\Gamma }_{0}\left(pq\right)$ with $p$ and $q$ distinct odd primes, giving an answer to a question of Merel in these cases. We also compute the winding elements explicitly for these congruence subgroups. Our results are explicit versions of the Manin–Drinfeld theorem.

Keywords
Eisenstein series, modular symbols, special values of $L$-functions
Mathematical Subject Classification 2010
Primary: 11F67
Secondary: 11F11, 11F20, 11F30