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                <term xml:lang="fr">forme modulaire presque holomorphe</term>
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                <term xml:lang="fr">forme quasimodulaire</term>
                <term xml:lang="fr">structure diﬀérentielle</term>
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              <p>This text is the result of a course given at the Centre international de rencontres mathématiques in Luminy from 26 to 30 may 2003. In the first chapter, we introduce the theory of modular forms with integral weight on Γ0(N). The second chapter is devoted to the study of periods of modular forms on Γ0(1) and the integral structures implied by these periods. In the third chapter the notions of quasi modular forms and quasi holomorphic modular forms on Γ0(1) are introduced as well as the links with differential operators. At least, the notion of half integral modular forms with multiplicative system is presented in an annex.</p>
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              <p>L'objet de ce cours est de présenter la théorie des formes modulaires et certains de ses développements récents. Dans un premier chapitre, on développe la théorie des formes modulaires sur les sous-groupes de congruence Γ 0 (N). Dans un deuxième chapitre, on présente la notion de périodes de formes modulaires sur le group modulaire. On en déduit des résultats concernant les structures rationnelles des espaces de formes modulaires. Dans une troisième partie, on étudie les structures différentielles sur les espaces de formes modulaires. C'est l'occasion de développer les notions de forme quasimodulaire et forme modulaire presque holomorphe introduites par Zagier. Enfin, en annexe, on étudie la théorie des formes modulaires avec systèmes multiplicatifs.</p>
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