A New Representation of the Riemann Zeta Function

Mahipal Gurram

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arXiv · 2510.27412

A New Representation of the Riemann Zeta Function

Mahipal Gurram

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Abstract

In this paper,we develop a novel representation of the zeta function expressed as the limiting difference between two structured double sums. This approach leads to a new and elegant identity involving maximum functions and additive terms, providing theoretical insights. The derivation relies on generalized harmonic series and polygamma functions, linking classical analysis with contemporary summation techniques.

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Mahipal Gurram. 2025-10-31. A New Representation of the Riemann Zeta Function. https://arxiv.org/abs/2510.27412

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