# Asymptotic Formulae for Mixed Congruence Stacks

## TL;DR

This paper extends the circle method to derive asymptotic formulas for mixed congruence unimodal sequences, revealing their growth behavior and distribution properties.

## Contribution

It introduces new asymptotic expansions for mixed congruence unimodal sequences using Wright's circle method and modular transformations.

## Key findings

- Asymptotic formulas for mixed congruence unimodal sequences derived
- Techniques include Wright's circle method and modular transformations
- Provides detailed asymptotic behavior of these sequences

## Abstract

Much like the important work of Hardy and Ramanujan proving the asymptotic formula for the partition function, Auluck and Wright 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 (mod m) and parts on the other side -r (mod m). Techniques used in the proofs include Wright's circle method, modular transformations, and bounding of complex integrals.