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Bounds for coefficients of the f(q) mock theta function and applications to partition ranks
Journal of Number Theory ( IF 0.6 ) Pub Date : 2021-03-10 , DOI: 10.1016/j.jnt.2021.01.009
Kevin Gomez , Eric Zhu

We compute effective bounds for α(n), the Fourier coefficients of Ramanujan's mock theta function f(q) utilizing a finite algebraic formula due to Bruinier and Schwagenscheidt. We then use these bounds to prove two conjectures of Hou and Jagadeesan on the convexity and maximal multiplicative properties of the even and odd partition rank counting functions.



中文翻译:

fq)模拟theta函数的系数界及其在分区秩中的应用。

我们计算有效边界 αñ,Ramanujan的模拟theta函数的傅立叶系数 Fq利用Bruinier和Schwagenscheidt提出的有限代数公式。然后,我们使用这些界限来证明Hou和Jagadeesan的两个猜想,它们关于偶数和奇数分区秩计数函数的凸性和最大乘性。

更新日期:2021-04-02
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