Remainder formula and zeta expression for extremal CFT partition functions

  • Floyd L. WilliamsEmail author
Part of the Progress in Mathematics book series (PM, volume 257)


We derive a remainder formula for the coefficients of modular invariant partition functions of extremal conformal field theories of central charge c = 24k, where k is a positive integer. The formula encodes, in particular, asymptotics of these coefficients and it provides for additional corrections to Bekenstein–Hawking black hole entropy. We also relate these partition functions to a Patterson–Selberg zeta function. More generally, when c is divisible by 8 we relate this zeta function to vacuum characters of affine E 8 and \(E_{8} \times E_{8}\).


Affine E8 Extremal conformal field theory Modular j-invariant q-expansion Black hole entropy Kloosterman sum Zeta function 

Mathematics Subject Classification

11FO3 11F25 11F30 11M36 81T40 81R10 83C57 


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of Massachusetts at AmherstAmherstUSA

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