We consider the problem of whether or not certain mock theta functions vanish at the roots of unity with an odd order. We prove for any such function f(q) that there exists a constant C> 0 such that for any odd integer n> C the function f(q) does not vanish at the primitive n-th roots of unity. This leads us to conjecture that f(q) does not vanish at the primitive n-th roots of unity for any odd positive integer n.
- Mock theta functions
- Vanishing sums of roots of unity
ASJC Scopus subject areas
- Algebra and Number Theory