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• W2765957314 abstract "We continue our study of a basic but seemingly intractable problem in integer partition theory, namely the conjecture that $p(n)$ is odd exactly $50%$ of the time. Here, we greatly extend on our previous paper by providing a doubly-indexed, infinite framework of conjectural identities modulo 2, and show how to, in principle, prove each such identity. However, our conjecture remains open in full generality. A striking consequence is that, under suitable existence conditions, if any $t$-multipartition function is odd with positive density and $tnot equiv 0$ (mod 3), then $p(n)$ is also odd with positive density. These are all facts that appear virtually impossible to show unconditionally today. Our arguments employ a combination of algebraic and analytic methods, including certain technical tools recently developed by Radu in his study of the parity of the Fourier coefficients of modular forms." @default.
• W2765957314 created "2017-11-10" @default.
• W2765957314 creator A5022091558 @default.
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• W2765957314 date "2017-10-27" @default.
• W2765957314 modified "2023-09-27" @default.
• W2765957314 title "On the density of the odd values of the partition function, II: An infinite conjectural framework" @default.
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• W2765957314 hasPublicationYear "2017" @default.
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