Abstract
In this paper, we present an algorithm to compute the deviation of the cranks from the average by using the theory of modular forms and Jacobi forms. Then applying the Ramanujan-type algorithm developed by Chen, Du and Zhao to each term in the expression of the deviation, we can derive the corresponding dissection formulas. As applications, we revisit the deviation of the cranks modulo 5 and 7, which were given by Garvan, and Mortenson, and also obtain the deviation of the cranks modulo 9 and 14.
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