Asymptotic formulae for mixed congruence stacks

  • Richard Frnka


Much like the important work of Hardy and Ramanujan (Proc Lond Math Soc 2(17):75–115, 1919) proving the asymptotic formula for the partition function, Auluck (Math Proc Camb Philos Soc 47:679–686, 1951) and Wright (Quart J Math (Oxf) 22:107–116, 1971) gave similar formulas for unimodal sequences. Following the circle method of Wright, we provide the asymptotic expansion for unimodal sequences on a two-parameter family of mixed congruence relations, with parts on one side up to the peak satisfying \(r \pmod {m}\) and parts on the other side \(-r\pmod {m}\). Techniques used in the proofs include Wright’s circle method, modular transformations, and bounding of complex integrals.


False theta functions Stacks Unimodal sequences Wright circle method 

Mathematics Subject Classification

05A15 05A16 05A17 11P81 11P82 



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Authors and Affiliations

  1. 1.Department of MathematicsLouisiana State UniversityBaton RougeUSA

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