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Algebraic de Rham theory for weakly holomorphic modular forms of level one. (English) Zbl 1422.11083

Summary: We establish an Eichler-Shimura isomorphism for weakly modular forms of level one. We do this by relating weakly modular forms with rational Fourier coefficients to the algebraic de Rham cohomology of the modular curve with twisted coefficients. This leads to formulae for the periods and quasiperiods of modular forms.

MSC:

11F11 Holomorphic modular forms of integral weight
11F23 Relations with algebraic geometry and topology
11F25 Hecke-Petersson operators, differential operators (one variable)
11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
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References:

[1] 10.1007/BF03343515 · Zbl 0035.06004 · doi:10.1007/BF03343515
[2] 10.1007/s00208-012-0816-y · Zbl 1312.11039 · doi:10.1007/s00208-012-0816-y
[3] 10.1007/s00208-014-1043-5 · Zbl 1320.11042 · doi:10.1007/s00208-014-1043-5
[4] 10.1007/s002220050051 · Zbl 0851.11030 · doi:10.1007/s002220050051
[5] ; Deligne, Équations différentielles à points singuliers réguliers. Lecture Notes in Math., 163 (1970) · Zbl 0244.14004
[6] 10.4310/PAMQ.2008.v4.n4.a15 · Zbl 1200.11027 · doi:10.4310/PAMQ.2008.v4.n4.a15
[7] 10.1007/BF01258863 · Zbl 0080.06003 · doi:10.1007/BF01258863
[8] 10.1090/S0002-9939-08-09277-0 · Zbl 1173.11028 · doi:10.1090/S0002-9939-08-09277-0
[9] 10.1007/978-3-540-37802-0_3 · doi:10.1007/978-3-540-37802-0_3
[10] 10.1515/9781400881710 · Zbl 0576.14026 · doi:10.1515/9781400881710
[11] 10.1090/tran/6595 · Zbl 1337.14021 · doi:10.1090/tran/6595
[12] ; Manin, Mat. Sb. (N.S.), 92(134), 378 (1973) · Zbl 0293.14007
[13] 10.1007/BF01388656 · Zbl 0553.10023 · doi:10.1007/BF01388656
[14] 10.2969/jmsj/01140291 · Zbl 0090.05503 · doi:10.2969/jmsj/01140291
[15] ; Swinnerton-Dyer, Modular functions of one variable, III. Lecture Notes in Math., 350, 1 (1973)
[16] 10.1007/978-3-540-74119-0_1 · Zbl 1259.11042 · doi:10.1007/978-3-540-74119-0_1
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