Exact formulae and Turán inequalities for Vafa-Witten invariants of K3 surfaces

Daniel R. Johnston; Joshua Males

doi:10.1017/S001309152300041X

Exact formulae and Turán inequalities for Vafa-Witten invariants of K3 surfaces

Daniel R. Johnston
, Joshua Males

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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 utilizing known properties of these η-functions, we obtain exact formulae for each of the invariants and prove that they asymptotically satisfy all higher-order Turán inequalities.

Original language	English
Pages (from-to)	845-861
Number of pages	17
Journal	Proceedings of the Edinburgh Mathematical Society
Volume	66
Issue number	3
DOIs	https://doi.org/10.1017/S001309152300041X
Publication status	Published - 8 Aug 2023

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math.NT

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10.1017/S001309152300041XLicence: Unspecified

https://arxiv.org/abs/2204.05465

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title = "Exact formulae and Tur{\'a}n 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 utilizing 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{\'a}n inequalities.",

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AB - 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 utilizing known properties of these η-functions, we obtain exact formulae for each of the invariants and prove that they asymptotically satisfy all higher-order Turán inequalities.

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U2 - 10.1017/S001309152300041X

DO - 10.1017/S001309152300041X

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EP - 861

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

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Exact formulae and Turán inequalities for Vafa-Witten invariants of K3 surfaces

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