Asymptotics of crank generating functions and Ramanujan congruences

2013/11/18 by Jose Miguel Zapata Rolon, Rolon, Jose Miguel Zapata
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.1311.4344

27 pages

arxiv created 2013/11/18 · arxiv updated 2013/11/19

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 can not explain any partition congruences in the usual way beside the three deduced by Ramanujan.

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