## Negative Weight Modular Forms and Black Hole Entropy: Logarithmic Corrections

We present a method of finding logarithmic corrections, up to an arbitrary order, of different quantities, such as black hole entropy in extreme CFT, or the entropy of p-branes compactified on a Kaluza-Klein space-time, by way of an elementary observation on the equivalent formulation of a certain asymptoticity in terms of a Bessel equation. In the more general mathematical context of negative weight modular forms, we indicate how some of the known work of physicists can be interpreted. A few minor mistakes are corrected in the literature. A good description of the paper is given in the concluding remarks in section 5.

**Author (s) Details**

**Floyd. L. Williams
**Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA01003, United States.

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black hole Dedekind eta function Eisenstein series extremal conformal field theory. Kloosterman sums Modular Forms p-brane entropy Riemann zeta function