Bounds for Coefficients of the f(q) Mock Theta Function and Applications to Partition Ranks

2020/08/19 by Kevin Gomez, Eric Zhu, Gomez, Kevin +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2008.08253

openalex publication_date 2020/08/19 · openalex created_date 2020/08/24 · openalex updated_date 2026/08/04

Abstract

We compute effective bounds for α(n), the Fourier coefficients of Ramunujan'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.

Citations

• Heegner points and derivatives ofL-series. II

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