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Journal Article

Periods of modular forms on Γ0(N) and products of Jacobi theta functions

MPS-Authors
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Zagier,  Don
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.4171/JEMS/864
(Publisher version)

Fulltext (public)

arXiv:1706.07885.pdf
(Preprint), 366KB

Supplementary Material (public)
There is no public supplementary material available
Citation

Choie, Y., Park, Y. K., & Zagier, D. (2019). Periods of modular forms on Γ0(N) and products of Jacobi theta functions. Journal of the European Mathematical Society, 21(5), 1379-1410. doi:10.4171/JEMS/864.


Cite as: http://hdl.handle.net/21.11116/0000-0004-864B-1
Abstract
Generalizing a result of [15] for modular forms of level one, we give a closed formula for the sum of all Hecke eigenforms on $\Gamma_0(N)$, multiplied by their odd period polynomials in two variables, as a single product of Jacobi theta series for any squarefree level $N$. We also show that for $N=2$,3 and 5 this formula completely determines the Fourier expansions of all Hecke eigenforms of all weights on $\Gamma_0(N)$.