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Wednesday 27 Sep 2023Title: The saddle-point solution for the general partition function

Madhuparna Das - University of Exeter

Newman Purple 14:30-15:30

Abstract: A partition of a number $n$ is an increasing sequence of integers whose sum is equal to $n$. It was introduced by Hardy-Ramanujan over a hundred years ago. Recently, Debruyne and Tenenbaum used saddle point solution to obtain asymptotic formula for generalized partition function associated with the Dirichlet series \[ L_\Lambda(z) =\sum_{m\in \Lambda} m^{-z}, \] where $\lambda\subset \mathbb{N}^*$. We give a brief overview of their proof and further discuss a generalization to Dirichlet series associated with multiplicative coefficient.

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