Class numbers, Jacobi forms and Siegel-Eisenstein series of weight 2 on Sp2 (ℤ)

Kohnen, Winfried

doi:10.1007/bf03025710

Cited by 10 publications

(3 citation statements)

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“…It would be very interesting to relate the black hole counting problems above to modular objects in a similar manner. In fact, the general statements of Kudla-Millson theory, as described in [35], encapsulate the count of attractor black holes in our example 2 in a degree 2 weight 2 Siegel form studied by Kohnen [34]. Kohnen's Sp(4, R) = Spin(3, 2) symmetry is a subgroup of the U-duality group SO(4, 3) of the corresponding three dimensional supergravity theory that was proposed as spectrum generating symmetry group of the 4d supergravity as mentioned above.…”

Section: Discussionsupporting

confidence: 60%

Black holes and Bhargava’s invariant theory

Günaydın¹,

Kachru

Tripathy

2020

J. Phys. A: Math. Theor.

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Attractor black holes in type II string compactifications on K3 × T 2 are in correspondence with equivalence classes of binary quadratic forms. The discriminant of the quadratic form governs the black hole entropy, and the count of attractor black holes at a given entropy is given by a class number. Here, we show this tantalizing relationship between attractors and arithmetic can be generalized to a rich family, connecting black holes in supergravity and string models with analogous equivalence classes of more general forms under the action of arithmetic groups. Many of the physical theories involved have played an earlier role in the study of 'magical' supergravities, while their mathematical counterparts are directly related to geometry-of-numbers examples in the work of Bhargava et al. This paper is dedicated to the memory of Peter Freund. The last section is devoted to some of MG's personal reminiscences of Peter Freund.

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Section: Discussionsupporting

confidence: 60%

Black holes and Bhargava’s invariant theory

Günaydın¹,

Kachru

Tripathy

2020

J. Phys. A: Math. Theor.

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“…A Fourier expansion of E (2) k (Z; s) has been already studied in [5,6,9]. However we derive different formula to separate holomorphic terms from non-holomorphic terms in the case of s = 0 after analytic continuation.…”

Section: Non-holomorphic Eisenstein Seriesmentioning

confidence: 97%

“…Note that the Fourier expansion of E (2) 2 (Z; 0) has been already studied in the different form (see [5]). Here we separate holomorphic terms and non-holomorphic terms.…”

Section: Main Correspondencementioning

confidence: 98%