Siegel modular forms of half integral weight and a lifting conjecture

Ibukiyama, Tomoyoshi; Hayashida, Shuichi

doi:10.1215/kjm/1250281971

Cited by 11 publications

(31 citation statements)

References 6 publications

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“…where for any given N , (ρ, σ, v) is a known function, transforming as a modular form of certain weight under a subgroup of Sp(2, Z) [43][44][45][46][47][48][49][50][51][52], and C is a three real dimensional subspace of the three complex dimensional space labelled by…”

Section: The Results For the Indexmentioning

confidence: 99%

How do black holes predict the sign of the Fourier coefficients of siegel modular forms?

Sen

2011

Gen Relativ Gravit

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Single centered supersymmetric black holes in four dimensions have spherically symmetric horizon and hence carry zero angular momentum. This leads to a specific sign of the helicity trace index associated with these black holes. Since the latter are given by the Fourier expansion coefficients of appropriate meromorphic modular forms of Sp(2, Z) or its subgroup, we are led to a specific prediction for the signs of a subset of these Fourier coefficients which represent contributions from single centered black holes only. We explicitly test these predictions for the modular forms which compute the index of quarter BPS black holes in heterotic string theory on T 6 , as well as in Z N CHL models for N = 2, 3, 5, 7.

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Section: The Results For the Indexmentioning

confidence: 99%

How do black holes predict the sign of the Fourier coefficients of siegel modular forms?

Sen

2011

Gen Relativ Gravit

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“…For M = K 3 and N = 2, 3 the function was found in [258][259][260]. A general discussion on construction of Siegel modular forms can be found in [261].…”

Section: Appendix A: the Sign Conventionsmentioning

confidence: 93%

Black hole entropy function, attractors and precision counting of microstates

2008

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In these lecture notes we describe recent progress in our understanding of attractor mechanism and entropy of extremal black holes based on the entropy function formalism. We also describe precise computation of the microscopic degeneracy of a class of quarter BPS dyons in N = 4 supersymmetric string theories, and compare the statistical entropy of these dyons, expanded in inverse powers of electric and magnetic charges, with a similar expansion of the corresponding black hole entropy. This comparison is extended to include the contribution to the entropy from multi-centred black holes as well.

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“…2. We note that the generators of the ring for Sp(2, Z), Γ 0 (2) and Γ ψ4 0 (4) have been already known in [17,12,11]. So for these groups, a new point here is that the fifth generator is obtained by a simple differential operator and has a Borcherds product expression.…”

Section: Introductionmentioning

confidence: 93%

Simple Graded Rings of Siegel Modular Forms, Differential Operators and Borcherds Products

2005

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In this paper, we show that the graded ring of Siegel modular forms of Γ 0 (N ) ⊂ Sp(2, Z) has a very simple unified structure for N = 1, 2, 3, 4, taking Neben-type case (the case with character) for N = 3 and 4. All are generated by 5 generators, and all the fifth generators are obtained by using the other four by means of differential operators, and it is also obtained as Borcherds products. As an appendix, examples of Euler factors of L-functions of Siegel modular forms of Sp(2, Z) of odd weight are given.

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Siegel modular forms of half integral weight and a lifting conjecture

Cited by 11 publications

References 6 publications

How do black holes predict the sign of the Fourier coefficients of siegel modular forms?

How do black holes predict the sign of the Fourier coefficients of siegel modular forms?

Black hole entropy function, attractors and precision counting of microstates

Simple Graded Rings of Siegel Modular Forms, Differential Operators and Borcherds Products

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