• 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… 
POWERS OF THE ETA-FUNCTION AND HECKE OPERATORS
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
TLDR
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.

References

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