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 Γ0(pq) 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
Milestones
Received: 14 April 2015
Revised: 25 June 2015
Accepted: 3 July 2015
Published: 16 February 2016
Authors
Debargha Banerjee
Department of Mathematics
Indian Institute of Science Education and Research, Pune
Pashan Road
Pashan
Pune 411008
India
Srilakshmi Krishnamoorthy
Department of Mathematics
Indian Institute of Technology Madras
Sardar Patel Road
Chennai
Adyar 600036
India