Nous présentons une interprétation géométrique d'une loi arithmétique pour déduire des formules explicites pour les coefficients des formes modulaires elliptiques et des formes de Jacobi. Nous discutons des applications de ces formules et comme exemple nous dérivons de manière algorithmique un critère analogue au critère de Tunnell concernant des nombres congruentes.
We give a geometric interpretation of an arithmetic rule to generate explicit formulas for the Fourier coefficients of elliptic modular forms and their associated Jacobi forms. We discuss applications of these formulas and derive as an example a criterion similar to Tunnel's criterion for a number to be a congruent number.
Mots clés : modular forms, jacobi forms, periods, special values, modular symbols
@article{JTNB_1991__3_1_93_0, author = {Nils-Peter Skoruppa}, title = {Heegner cycles, modular forms and jacobi forms}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {93--116}, publisher = {Universit\'e Bordeaux I}, volume = {3}, number = {1}, year = {1991}, zbl = {0734.11033}, mrnumber = {1116103}, language = {en}, url = {https://jtnb.centre-mersenne.org/item/JTNB_1991__3_1_93_0/} }
TY - JOUR AU - Nils-Peter Skoruppa TI - Heegner cycles, modular forms and jacobi forms JO - Journal de théorie des nombres de Bordeaux PY - 1991 SP - 93 EP - 116 VL - 3 IS - 1 PB - Université Bordeaux I UR - https://jtnb.centre-mersenne.org/item/JTNB_1991__3_1_93_0/ LA - en ID - JTNB_1991__3_1_93_0 ER -
Nils-Peter Skoruppa. Heegner cycles, modular forms and jacobi forms. Journal de théorie des nombres de Bordeaux, Tome 3 (1991) no. 1, pp. 93-116. https://jtnb.centre-mersenne.org/item/JTNB_1991__3_1_93_0/
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