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arXiv · 2609.00537

Explicit Exponential Sum Estimates and Approximate Functional Equations for the Zeta Function

Natasha Dhiman·Habiba Kadiri·Emily Quesada-Herrera
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Abstract

We show an explicit version of the Van der Corput truncated Poisson summation formula (B-process). By using refined explicit exponential sum estimates, this improves the error term of previous explicit results by Patel and Yang (2024) and Arias de Reyna (2024). As an application, we obtain fine explicit estimates for the error terms in approximate functional equations for the Riemann zeta function, improving on previous explicit results of Simonič (2020) in certain ranges.

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Natasha Dhiman, Habiba Kadiri, Emily Quesada-Herrera. 2026-09-01. Explicit Exponential Sum Estimates and Approximate Functional Equations for the Zeta Function. https://arxiv.org/abs/2609.00537

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