Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.00537

Authors: Dhiman, Natasha, Kadiri, Habiba, Quesada-Herrera, Emily

Institution: University of Lethbridge

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7206216267

Cites: 1

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Related to: 10