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Explicit Exponential Sum Estimates and Approximate Functional Equations for the Zeta Function
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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BibTeX
@misc{dhiman2026explicit,
title = {{Explicit Exponential Sum Estimates and Approximate Functional Equations for the Zeta Function}},
author = {Natasha Dhiman and Habiba Kadiri and Emily Quesada-Herrera},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00537},
eprint = {2609.00537},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00537},
}
RIS
TY - UNPB
TI - Explicit Exponential Sum Estimates and Approximate Functional Equations for the Zeta Function
AU - Natasha Dhiman
AU - Habiba Kadiri
AU - Emily Quesada-Herrera
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.00537
UR - https://arxiv.org/abs/2609.00537
AB - 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.
ER -