$f(x) =\sum_{n=0}^{\infty} x^{n^2}$ and similar "theta-type" functions are extensively studied. They have many properties and occur in number theory , algebra (in particular solving the quintic without hypergeometric functions) , calculus ($q$-analogues) and physics.
But what is known about $g(x) =\sum_{n=0}^{\infty} x^{n^3}$?
Is that not interesting ? If not, why not ?
I'm confused about this.
Hope this a good question.
For all clarity I'm not asking for demonstrations about $f(x)$ , I know it has many properties.
Too add a more specific question , why doesn't $g(x)$ occur in solving polynomials of degree $>5$?