Exact formulae and Tur\'an inequalities for Vafa-Witten invariants of K3 surfaces
Abstract
We consider three different families of Vafa-Witten invariants of K3 surfaces. In each case, the partition function that encodes the Vafa-Witten invariants is given by combinations of twisted Dedekind η-functions. By utilising known properties of these η-functions, we obtain exact formulae for each of the invariants and prove that they asymptotically satisfy all higher-order Tur\'an inequalities.
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