@**article**{RISC6342,author = {Ralf Hemmecke and Peter Paule and Silviu Radu},

title = {{Construction of modular function bases for $Gamma_0(121)$ related to $p(11n+6)$}},

language = {english},

abstract = {Motivated by arithmetic properties of partition
numbers $p(n)$, our goal is to find algorithmically
a Ramanujan type identity of the form
$sum_{n=0}^{infty}p(11n+6)q^n=R$, where $R$ is a
polynomial in products of the form
$e_alpha:=prod_{n=1}^{infty}(1-q^{11^alpha n})$
with $alpha=0,1,2$. To this end we multiply the
left side by an appropriate factor such the result
is a modular function for $Gamma_0(121)$ having
only poles at infinity. It turns out that
polynomials in the $e_alpha$ do not generate the
full space of such functions, so we were led to
modify our goal. More concretely, we give three
different ways to construct the space of modular
functions for $Gamma_0(121)$ having only poles at
infinity. This in turn leads to three different
representations of $R$ not solely in terms of the
$e_alpha$ but, for example, by using as generators
also other functions like the modular invariant $j$.},

journal = {Integral Transforms and Special Functions},

volume = {32},

number = {5-8},

pages = {512--527},

publisher = {Taylor & Francis},

isbn_issn = {1065-2469},

year = {2021},

refereed = {yes},

keywords = {Ramanujan identities, bases for modular functions, integral bases},

sponsor = {FWF (SFB F50-06)},

length = {16},

url = {https://doi.org/10.1080/10652469.2020.1806261}

}