Universal mock theta functions as quantum Jacobi forms View Full Text


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Article Info

DATE

2019-03

AUTHORS

Greg Carroll, James Corbett, Amanda Folsom, Ellie Thieu

ABSTRACT

Quantum Jacobi forms were defined in 2016, naturally combining Zagier’s definition of a quantum modular form with that of a Jacobi form. To date, just three examples of such functions exist in the literature. Here, we prove that the universal mock theta function g2, as well as the universal mock theta functions K,K1,K2, and κ, gives rise to an infinite family of quantum Jacobi forms Ga,b(z;τ) of weight 1 / 2 in dense subsets Qa,b⊆Q×Q. We then use these quantum Jacobi transformation properties to establish polynomial expressions for Ga,b at pairs of rational numbers, as well as simple closed-form expressions for sums of Mordell integrals. More... »

PAGES

6

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URI

http://scigraph.springernature.com/pub.10.1007/s40687-018-0169-6

DOI

http://dx.doi.org/10.1007/s40687-018-0169-6

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https://app.dimensions.ai/details/publication/pub.1110203755


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