Search results
Results From The WOW.Com Content Network
In mathematics, a mock modular form is the holomorphic part of a harmonic weak Maass form, and a mock theta function is essentially a mock modular form of weight 1 / 2 . The first examples of mock theta functions were described by Srinivasa Ramanujan in his last 1920 letter to G. H. Hardy and in his lost notebook .
The majority of the formulas are about q-series and mock theta functions, about a third are about modular equations and singular moduli, and the remaining formulas are mainly about integrals, Dirichlet series, congruences, and asymptotics. The mock theta functions in the notebook have been found to be useful for calculating the entropy of black ...
Sander Pieter Zwegers (born April 16, 1975) is a Dutch mathematician who made a connection between Maass forms and Srinivasa Ramanujan's mock theta functions in 2002. [1] [2] He was born in Oosterhout. After a period at the Max-Planck Institute in Bonn, he became an assistant professor at the University College Dublin in 2008.
In mathematics, particularly q-analog theory, the Ramanujan theta function generalizes the form of the Jacobi theta functions, while capturing their general properties. In particular, the Jacobi triple product takes on a particularly elegant form when written in terms of the Ramanujan theta. The function is named after mathematician Srinivasa ...
In the mathematical description of general relativity, the Boyer–Lindquist coordinates [1] are a generalization of the coordinates used for the metric of a Schwarzschild black hole that can be used to express the metric of a Kerr black hole. The Hamiltonian for particle motion in Kerr spacetime is separable in Boyer–Lindquist coordinates.
II. Theta functions of even unimodular lattices. An even unimodular lattice L in R n is a lattice generated by n vectors forming the columns of a matrix of determinant 1 and satisfying the condition that the square of the length of each vector in L is an even integer. The so-called theta function
These minimality properties imply the mock modular forms are uniquely determined by their shadows, which are vector-valued theta series constructed from the root system. The special case where X is the A 1 24 root system yields precisely Mathieu Moonshine. The umbral moonshine conjecture has been proved in Duncan, Griffin & Ono (2015).
The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon.The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear, which makes exact solutions very difficult to find.