• Corpus ID: 10775974

# THE PARTITION FUNCTION AND HECKE OPERATORS

@inproceedings{Ono2011THEPF,
title={THE PARTITION FUNCTION AND HECKE OPERATORS},
author={Ken Ono},
year={2011}
}
• K. Ono
• Published 2011
• Mathematics
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…
2 Citations
POWERS OF THE ETA-FUNCTION AND HECKE OPERATORS
• Mathematics
• 2012
Half-integer weight Hecke operators and their distinct properties play a major role in the theory surrounding partition numbers and Dedekind's eta-function. Generalizing the work of Ono in [K. Ono,
Congruences for Andrews' spt-Function Modulo 32760 and Extension of Atkin's Hecke-Type Partition Congruences
• F. Garvan
• Mathematics
Number Theory and Related Fields
• 2013
These results depend on the recent result of Ono that $$\mathcal{M}_{\ell}(z/24)$$ is a weakly holomorphic modular form of weight $$\tfrac{3} {2}$$ for the full modular group.

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