Modular symbols and Petersson’s product. (Symboles modulaires et produit de Petersson.) (French. English summary) Zbl 1468.11098
Summary: We revisit some papers by Eichler and Shimura in order to give an algebraic formulation (based on Farey symbols) for the intersection product on the space of modular symbols, as described by R. Pollack and G. Stevens [Ann. Sci. Éc. Norm. Supér. (4) 44, No. 1, 1–42 (2011; Zbl 1268.11075)]. We define the period homomorphism of an Eisenstein series (Eisenstein-Dedekind-Stevens symbol) and extend the definition of the intersection product to these objects. We construct a computationally convenient basis for the space of Eisenstein series for \(\Gamma_0(N)\) with rational periods. Given a Farey symbol for a subgroup \(\Gamma\) of the modular group and a subgroup \(\Gamma'\) of finite index of \(\Gamma\), we give an algorithmic construction for a Farey symbol for \(\Gamma'\).
MSC:
| 11F03 | Modular and automorphic functions |
| 11F11 | Holomorphic modular forms of integral weight |
| 11F67 | Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols |
| 11F30 | Fourier coefficients of automorphic forms |
Citations:
Zbl 1268.11075Software:
PARI/GPReferences:
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