History
Much of the early work establishing the convergence and equivalence of series regularized with the heat kernel and zeta function regularization methods was done by G.H. Hardy and J. E. Littlewood in 1916 and is based on the application of the Cahen–Mellin integral. The effort was made in order to obtain values for various ill-defined, conditionally convergent sums appearing in number theory.
Read more about this topic: Zeta Function Regularization
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