I was awarded a grant from the University of Exeter and the London Mathematical Society and spent the summer between my third and fourth years of my undergraduate degree conducting research alongside Julio Andrade. My research over the summer is summarised in this paper.
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Abstract:
In this paper, we consider a general form of the analogue of Ramanujan’s sum in the ring of polynomials over a finite field. We first prove some multiplicative properties of such functions before considering their finite Fourier series and some specific examples. In the end we also prove a result about the Dirichlet series of such functions.
Citation:
Andrade, J. C. and Hanslope, J. R. P. 2019. “Generalisations of Ramanujan Sums for Polynomial Rings Over Finite Fields” arXiv preprint arXiv:1909.12747 https://arxiv.org/abs/1909.12747