Author
Bellaïche, J
Green, B
Soundararajan, K
Journal title
Research in the Mathematical Sciences
DOI
10.1007/s40687-018-0123-7
Volume
5
Last updated
2023-12-15T00:12:37.173+00:00
Abstract
We obtain new lower bounds for the number of Fourier coefficients of a weakly holomorphic modular form of half-integral weight not divisible by some prime $\ell$. Among the applications of this we show that there are $\gg \sqrt{X}/\log \log X$ integers $n \leq X$ for which the partition function $p(n)$ is not divisible by $\ell$, and that there are $\gg \sqrt{X}/\log \log X$ values of $n \leq X$ for which $c(n)$, the $n$th Fourier coefficient of the $j$-invariant, is odd.
Symplectic ID
715822
Favourite
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Publication type
Journal Article
Publication date
31 Jan 2018
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