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August 2, 2026Open Access

Partial sums of the Legendre symbol at rational points: The master functional equation, the real mirror, the descent lemma and the ramification criterion

Jorge Vicente Romero

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Key Points

This research aims to explore new advances concerning partial sums of the Legendre symbol at rational points.
Discussed the master functional equation related to the Legendre symbol.
Applied the descent lemma in the context of rational points.
Analyzed the ramification criterion to derive conclusions on the properties of the Legendre symbol.
Presented new insights into the behavior of partial sums of the Legendre symbol.
Demonstrated connections between the Legendre symbol and rational points.
Highlighted the implications of the master functional equation in this context.

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Implication

New advances in understanding the Legendre symbol and its implications for rational points, suggesting novel mathematical insights.

Abstract

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Cite This Study

Jorge Vicente Romero (2026) studied this question.

synapsesocial.com/papers/6a719922c47350ef8e4948fd https://doi.org/10.5281/zenodo.21758732

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Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

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4Liouville Function Partial Sums as a Sufficient Condition for the Riemann Hypothesis — E8 Intelligence ResearchOriginal Research · 2026
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