Asymptotic equidistribution and convexity for partition ranks

DOI10.1007/s11139-019-00202-8zbMath1468.11214arXiv1903.05857OpenAlexW3000962421WikidataQ126302048 ScholiaQ126302048MaRDI QIDQ829696

Joshua Males

Publication date: 6 May 2021

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.05857

zbMATH Keywords

partitionsasymptoticsAppell functionpartition rank

Mathematics Subject Classification ID

Analytic theory of partitions (11P82)

Related Items (12)

Asymptotics, Turán inequalities, and the distribution of the BG-rank and 2-quotient rank of partitions ⋮ Strict log-subadditivity for overpartition rank ⋮ Exact formulae and Turán inequalities for Vafa–Witten invariants of surfaces ⋮ Log-concavity of the restricted partition function \(p_{\mathcal{A}}(n, k)\) and the new Bessenrodt-Ono type inequality ⋮ New equalities and inequalities for the ranks and cranks of partitions ⋮ Asymptotic equidistribution for partition statistics and topological invariants ⋮ Inequalities for plane partitions ⋮ Bounds for coefficients of the \(f(q)\) mock theta function and applications to partition ranks ⋮ Asymptotic distribution of odd balanced unimodal sequences with rank congruent to \(a\) modulo \(c\) ⋮ Proof of the Bessenrodt-Ono inequality by induction ⋮ Asymptotics for the twisted eta-product and applications to sign changes in partitions ⋮ Uniform asymptotic formulas for the Fourier coefficients of the inverse of theta functions

Cites Work

• Unnamed Item
• Maximal multiplicative properties of partitions
• Dyson's ranks and Maass forms
• Dyson's partition ranks and their multiplicative extensions
• Asymptotic formulas related to the \(M_2\)-rank of partitions without repeated odd parts
• Multivariable Appell functions and nonholomorphic Jacobi forms
• Inequalities for ranks of partitions and the first moment of ranks and cranks of partitions
• A Tauberian theorem for partitions
• Harmonic Maass Forms and Mock Modular Forms: Theory and Applications
• Asymptotics for rank partition functions
• New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
• Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura

This page was built for publication: Asymptotic equidistribution and convexity for partition ranks