The Eisenstein and winding elements of modular symbols for odd square-free level. (English) Zbl 1517.11051
Summary: We explicitly write down the Eisenstein elements inside the space of modular symbols for Eisenstein series with integer coefficients for the congruence subgroups \(\Gamma_0(N)\) with \(N\) odd square-free. We also compute the winding elements explicitly for these congruence subgroups. Our results are explicit versions of the Manin-Drinfeld Theorem (Thm. 6). These results are the generalization of the paper [D. Banerjee and the author, Pac. J. Math. 281, No. 2, 257–285 (2016; Zbl 1341.11023)] results to odd square-free level.
MSC:
| 11F67 | Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols |
| 11F11 | Holomorphic modular forms of integral weight |
| 11F20 | Dedekind eta function, Dedekind sums |
| 11F30 | Fourier coefficients of automorphic forms |
Citations:
Zbl 1341.11023References:
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