POWERS OF THE ETA-FUNCTION AND HECKE OPERATORS
2012 ◽
Vol 08
(03)
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pp. 599-611
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Keyword(s):
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, The partition function and Hecke operators, Adv. Math.228 (2011) 527–534], here we obtain closed formulas for the Hecke images of all negative powers of the eta-function. These formulas are generated through the use of Faber polynomials. In addition, congruences for a large class of powers of Ramanujan's Delta-function are obtained in a corollary. We further exhibit a fast calculation for many large values of vector partition functions.
2010 ◽
Vol 06
(02)
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pp. 281-309
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Keyword(s):
1991 ◽
Vol 06
(15)
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pp. 2743-2754
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Keyword(s):