Mock modular forms and geometric theta functions for indefinite quadratic forms. (English) Zbl 1376.81058
Summary: Mock modular forms are central objects in the recent discoveries of new instances of Moonshine. In this paper, we discuss the construction of mixed mock modular forms via integrals of theta series associated to indefinite quadratic forms. In particular, in this geometric setting, we realize Zwegers’ Mock theta functions of type \((p,1)\) as line integrals in hyperbolic \(p\)-space.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 11F27 | Theta series; Weil representation; theta correspondences |
| 11E16 | General binary quadratic forms |
| 11F55 | Other groups and their modular and automorphic forms (several variables) |
| 17B67 | Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras |
| 81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |
| 11F22 | Relationship to Lie algebras and finite simple groups |
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