Research Projects

Recently, for the purpose of proving the reciprocity law of the fourier-Dedekind sum (appearing in restricted partition) we used a a novel route of commutative algebra. This approach not only gave us the proof but also a generalization! Furthermore these techniques are also leading us to some interesting results in generating functions. Our methodology is based on the localization and I-adic completion of commutative rings. In this project, we wish to use this novel commutative algebra approach to generating functions. We find that it has a lot of potential in terms of obtaining direct formulae and also leading to the so-called Umbral Calculus. We also find that our approach can be extended to hypergeometric functions. Recently, we found an application of our work to Deletion Correction Codes. Our work is also amenable to computations tools such as SgaeMath.