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Congruences for a mock modular form on $\operatorname{SL}_2(\mathbb{Z})$ and the smallest parts function. (arXiv:1706.07453v1 [math.NT])
来源于:arXiv
Using a family of mock modular forms constructed by Zagier, we study the
coefficients of a mock modular form of weight $3/2$ on
$\operatorname{SL}_2(\mathbb{Z})$ modulo primes $\ell\geq 5$. These
coefficients are related to the smallest parts function of Andrews. As an
application, we reprove a theorem of Garvan regarding the properties of this
function modulo $\ell$. As another application, we show that congruences modulo
$\ell$ for the smallest parts function are rare in a precise sense. 查看全文>>