2016/02/09 by Bhattacharya, Soumya
#11F11 (Primary) #11F12 (Secondary) #11F20 #11F37 #11G16 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1602.02835
We give a short proof of Zagier's conjecture / Mersmann's theorem which states that each holomorphic eta quotient of weight 1/2 is an integral rescaling of some eta quotient from Zagier's list of fourteen primitive holomorphic eta quotients. In particular, given any holomorphic eta quotient f of weight 1/2, this result enables us to provide a closed-form expression for the coefficient of qn in the q-series expansion of f, for all n. We also demonstrate another application of the above theorem in extending the levels of the simple (resp. irreducible) holomorphic eta quotients.