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- W4311641574 abstract "It is widely believed that the parity of the partition function $p(n)$ is ``random.'' Contrary to this expectation, in this note we prove the existence of infinitely many congruence relations modulo 4 among its values. For each square-free integer $1<Dequiv 23pmod{24},$ we construct a weight 2 meromorphic modular form that is congruent modulo 4 to a certain twisted generating function for the numbers $pbig(frac{Dm^2+1}{24}big)pmod 4$. We prove the existence of infinitely many linear dependence congruences modulo 4 among suitable sets of holomorphic normalizations of these series. These results rely on the theory of class numbers and Hilbert class polynomials, and {it generalized twisted Borcherds products} developed by Bruinier and the author." @default.
- W4311641574 created "2022-12-27" @default.
- W4311641574 creator A5042566789 @default.
- W4311641574 date "2022-12-13" @default.
- W4311641574 modified "2023-09-26" @default.
- W4311641574 title "The partition function modulo 4" @default.
- W4311641574 doi "https://doi.org/10.48550/arxiv.2212.06935" @default.
- W4311641574 hasPublicationYear "2022" @default.
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