Algebraic de Rham theory for weakly holomorphic modular forms of level one
Copyright policy )Algebraic de Rham theory for weakly holomorphic modular forms of level one
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 quasi-periods of modular forms.
25 pages: final version; added references and several minor corrections
- THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD United Kingdom
- Duke University United States
- University of Oxford United Kingdom
Mathematics - Number Theory, weakly holomorphic modular form, 11F11 (Primary) 11F23, 11F25 (Secondary), 11F23, 11F67, Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, 11F11, algebraic de Rham cohomology, Relations with algebraic geometry and topology, Mathematics - Algebraic Geometry, 11F25, FOS: Mathematics, Hecke-Petersson operators, differential operators (one variable), Number Theory (math.NT), Holomorphic modular forms of integral weight, Algebraic Geometry (math.AG)
Mathematics - Number Theory, weakly holomorphic modular form, 11F11 (Primary) 11F23, 11F25 (Secondary), 11F23, 11F67, Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, 11F11, algebraic de Rham cohomology, Relations with algebraic geometry and topology, Mathematics - Algebraic Geometry, 11F25, FOS: Mathematics, Hecke-Petersson operators, differential operators (one variable), Number Theory (math.NT), Holomorphic modular forms of integral weight, Algebraic Geometry (math.AG)
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