Abstract
In this paper we obtain asymptotic formulas for the Fourier coefficients of an infinite family of crank-generating functions. Moreover, we use this result to show that the crank obeys certain inequalities. This implies that the crank cannot explain any partition congruences in the usual way beside the three deduced by Ramanujan.
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Notes
we will make this statement more precise in the next section, see (4.6)
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Acknowledgments
I would like to thank Prof. Dr. Kathrin Bringmann for suggesting me the topic as a diploma thesis and for many helpful discussions. Moreover I would like to thank Dr. Ben Kane for many helpful discussions and Michael Mertens for useful comments on the paper.
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Zapata Rolon, J.M. Asymptotics of crank generating functions and Ramanujan congruences. Ramanujan J 38, 147–178 (2015). https://doi.org/10.1007/s11139-014-9582-7
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DOI: https://doi.org/10.1007/s11139-014-9582-7