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arXiv · 1608.01765

Exact Russell-Type Modular Equations

Timothy Redmond·Charles Ryavec
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Abstract

This paper provides some statistics for the coefficients of Russell- Type modular equations for the modular function, {\lambda}({\tau}). The results hold uniformly for all odd primes. They do not rely on any numerical evaluations of coefficients of q expansions of {\lambda}. The method relies on an internal structure of the coefficients of {\lambda} expressed in terms of multiplicative functions defined on integer partitions. The method may be extended to other types of modular equations.

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Timothy Redmond, Charles Ryavec. 2016-08-05. Exact Russell-Type Modular Equations. https://arxiv.org/abs/1608.01765

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