How to Compute the Coefficients of the Elliptic Modular Function j(z)

Baier, Harald; Köhler, Günter

Experiment. Math., Tome 12 (2003) no. 1, p. 115-128 / Harvested from Project Euclid

Résumé

We discuss various methods to compute the Fourier coefficients of the elliptic modular function j(z). We present run times to compute the coefficients in practice. If possible, we discuss the theoretical complexity of the corresponding method, too. We conclude that, in practice, an approach due to Kaneko and Zagier turns out to be most efficient.

Publié le : 2003-05-14
Classification: Algorithmic number theory, elliptic modular function $j$, Fourier coefficients, Fourier series, 42A16, 11F03

@article{1064858788,
     author = {Baier, Harald and K\"ohler, G\"unter},
     title = {How to Compute the Coefficients of the Elliptic Modular Function j(z)},
     journal = {Experiment. Math.},
     volume = {12},
     number = {1},
     year = {2003},
     pages = { 115-128},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1064858788}
}

Baier, Harald; Köhler, Günter. How to Compute the Coefficients of the Elliptic Modular Function j(z). Experiment. Math., Tome 12 (2003) no. 1, pp.  115-128. http://gdmltest.u-ga.fr/item/1064858788/