Geodesic
Eulerian series as modular forms
Bringmann, Kathrin1 ; Ono, Ken2 ; Rhoades, Robert2
1 School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
2 Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Journal of the American Mathematical Society, Tome 21 (2008) no. 4, pp. 1085-1104

Voir la notice de l'article provenant de la source American Mathematical Society

In 1988, Hickerson proved the celebrated “mock theta conjectures” in a collection of ten identities from Ramanujan’s “lost notebook” which express certain modular forms as linear combinations of mock theta functions. In the context of Maass forms, these identities arise from the peculiar phenomenon that two different harmonic Maass forms may have the same non-holomorphic parts. Using this perspective, we construct several infinite families of modular forms which are differences of mock theta functions.
DOI : 10.1090/S0894-0347-07-00587-5

Bringmann, Kathrin 1 ; Ono, Ken 2 ; Rhoades, Robert 2

1 School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
2 Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706 
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Bringmann, Kathrin; Ono, Ken; Rhoades, Robert. Eulerian series as modular forms. Journal of the American Mathematical Society, Tome 21 (2008) no. 4, pp. 1085-1104. doi: 10.1090/S0894-0347-07-00587-5

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