Ternary polynomial relations and periods of cusp forms

Vasily Ilin, Ken Ono

Bachmann and van Ittersum conjectured that every polynomial $f\in \mathbb{Q}[x,y,z]$ satisfying $$f(x,y,z)=f(y,z,x),f(x,y,z)+f(-y,x-y,z)+f(y-x,-x,z)=0$$ is a sum of polynom…