# Landau–Siegel zeroes and black hole entropy

@article{Miller1999LandauSiegelZA, title={Landau–Siegel zeroes and black hole entropy}, author={Stephen D. Miller and Gregory Moore}, journal={Asian Journal of Mathematics}, year={1999}, volume={4}, pages={183-212} }

There has been some speculation about relations of D-brane models of black holes to arithmetic. In this note we point out that some of these speculations have implications for a circle of questions related to the generalized Riemann hypothesis on the zeroes of Dirichlet $L$-functions.

## 20 Citations

### A Black Hole Farey Tail

- Mathematics
- 2000

We derive an exact expression for the Fourier coefficients of elliptic genera of Calabi-Yau manifolds. When applied to k-fold symmetric products of K3 surfaces the expression is well-suited to…

### Precision Counting of Small Black Holes

- Physics
- 2005

It has recently been proposed that a class of supersymmetric higher-derivative interactions in = 2 supergravity may encapsulate an infinite number of finite size corrections to the microscopic…

### Exact and Asymptotic Degeneracies of Small Black Holes

- Physics
- 2005

We examine the recently proposed relations between black hole entropy and the topological string in the context of type II/heterotic string dual models. We consider the degeneracies of perturbative…

### Calabi–Yau Black Holes and (0,4) Sigma Models

- Mathematics
- 1999

Abstract:When an M-theory fivebrane wraps a holomorphic surface ? in a Calabi–Yau 3-fold X the low energy dynamics is that of a black string in 5 dimensional ? =1 supergravity. The infrared dynamics…

### 2 M ar 2 00 3 Complex Multiplication Symmetry of Black Hole Attractors

- Mathematics
- 2003

We show how Moore’s observation, in the context of toroidal compactifications in type IIB string theory, concerning the complex multiplication structure of black hole attractor varieties, can be…

### Arithmetic and Attractors

- Mathematics
- 1998

We study relations between some topics in number theory and supersymmetric black holes. These relations are based on the ``attractor mechanism'' of N=2 supergravity. In IIB string compactification…

### Extremal N = (2, 2) 2D Conformal Field Theories and Constraints of Modularity

- Mathematics
- 2008

We explore the constraints on the spectrum of primary fields implied by modularity of the elliptic genus of N = (2, 2) 2D CFT’s. We show that such constraints have nontrivial implications for the…

### A non-split sum of coefficients of modular forms

- Mathematics
- 2009

We shall introduce and study certain truncated sums of Hecke eigenvalues of $GL_2$-automorphic forms along quadratic polynomials. A power saving estimate is established and new applications to…

### Rational Conformal Field Theories and Complex Multiplication

- Mathematics
- 2004

We study the geometric interpretation of two dimensional rational conformal field theories, corresponding to sigma models on Calabi-Yau manifolds. We perform a detailed study of RCFT’s corresponding…

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We study relations between some topics in number theory and supersymmetric black holes. These relations are based on the ``attractor mechanism'' of N=2 supergravity. In IIB string compactification…