A Rademacher-type exact formula for partitions without sequences

2023/04/03 by Walter Bridges, Kathrin Bringmann, Bridges, Walter +1 · 1 citation
Mathematics · #Advanced Mathematical Identities #Advanced Combinatorial Mathematics #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.2304.01377

Abstract

In this paper we prove an exact formula for the number of partitions without sequences. By work of Andrews, the corresponding generating function is a product of a modular form and a mock theta function, giving an overall weight of 0. The proof requires evaluating and bounding Kloosterman sums and the Circle Method

Cited by

• A generic approach to proving Turán-type inequalities for sequences that admit exact formulas, with an application to unimodal sequences

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• Short proof of Rademacher's formula for partitions
• Distinct parts partitions without sequences
• Exact formulae for ranks of partitions
• Rademacher's Formula for the Partition Function
• Exact Formulae for the Fractional Partition Functions