author = {Ralf Hemmecke and Silviu Radu},
title = {{Construction of all Polynomial Relations among Dedekind Eta Functions of Level $N$}},
language = {english},
abstract = {We describe an algorithm that, given a positive integer $N$, computes a Gr\"obner basis of the ideal of polynomial relations among Dedekind $\eta$-functions of level $N$, i.e., among the elements of $\{\eta(\delta_1\tau),\ldots,\eta(\delta_n\tau)\}$ where $1=\delta_1<\delta_2\dots<\delta_n=N$ are the positive divisors of $N$. More precisely, we find a finite generating set (which is also a Gr\"obner basis of the ideal $\ker\phi$ where \begin{gather*} \phi:Q[E_1,\ldots,E_n] \to Q[\eta(\delta_1\tau),\ldots,\eta(\delta_n\tau)], \quad E_k\mapsto \eta(\delta_k\tau), \quad k=1,\ldots,n. \end{gather*} },
journal = {Journal of Symbolic Compuation},
volume = {95},
pages = {39--52},
isbn_issn = {ISSN 0747-7171},
year = {2019},
note = {Also available as RISC Report 18-03 http://www.risc.jku.at/publications/download/risc_5561/etarelations.pdf},
refereed = {yes},
keywords = {Dedekind $\eta$ function, modular functions, modular equations, ideal of relations, Groebner basis},
length = {14},
url = {https://doi.org/10.1016/j.jsc.2018.10.001}