The Partition Function and Hecke Operators
نویسنده
چکیده
The theory of congruences for the partition function p(n) depends heavily on the properties of half-integral weight Hecke operators. The subject has been complicated by the absence of closed formulas for the Hecke images P (z) | T (`), where P (z) is the relevant modular generating function. We obtain such formulas using Euler’s Pentagonal Number Theorem and the denominator formula for the Monster Lie algebra. As a corollary, we obtain congruences for certain powers of Ramanujan’s Delta-function.
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