\(q\)-series, elliptic curves, and odd values of the partition function (Q1283402)

Let \(p(n)\) denote the partition function. Using the theory of elliptic curves over finite fields as well as \(q\)-series, the author proves 8 theorems including the following: Let \(n\) be an odd square. Let \(S_n= \{1,2,3,\dots,{1\over 4}(n- 1)\}\). Then \(S_n\) has a subsequence, \(T_n\), such that \(p(k)\) is odd for oddly many \(k\) in \(T_n\).