A Comprehensive Review of the Riemann Hypothesis: Analytic Advances, Computational Verification, and Interdisciplinary Connections

Jiale Liu

doi:10.47297/taposatWSP2633-456927.20250603

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A Comprehensive Review of the Riemann Hypothesis: Analytic Advances, Computational Verification, and Interdisciplinary Connections

Volume 6, Issue 3

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A Comprehensive Review of the Riemann Hypothesis: Analytic Advances, Computational Verification, and Interdisciplinary Connections
A Comprehensive Review of the Riemann Hypothesis: Analytic Advances, Computational Verification, and Interdisciplinary Connections
Central South University, Hunan ChangSha, 410006
Vol. 6, Issue 3, Pages: 138-144(2025)
Published：25 March 2025
DOI：10.47297/taposatWSP2633-456927.20250603
Accepted：

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Liu Jiale.A Comprehensive Review of the Riemann Hypothesis: Analytic Advances, Computational Verification, and Interdisciplinary Connections[J].Theory and Practice of Science and Technology,2025,06(03):138-144.
DOI：

Liu Jiale.A Comprehensive Review of the Riemann Hypothesis: Analytic Advances, Computational Verification, and Interdisciplinary Connections[J].Theory and Practice of Science and Technology,2025,06(03):138-144. DOI： 10.47297/taposatWSP2633-456927.20250603.

摘要

Abstract

Since its inception in 1859

the Riemann Hypothesis (RH) has remained central to number theory. This paper systematically reviews milestone advancements

from Hardy's proof of the existence of zeros on the critical line to the Levinson-Conrey optimization of zero density proportions

and the Montgomery-Odlyzko correlations with statistical mechanics. By integrating computational verification and quantum chaos models

we explore modern interpretations of RH in algebraic geometry and noncommutative geometry. Synthesizing landmarks achievements since the 20th century

this work reveals potential pathways for multidisciplinary approaches to resolving RH.

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references

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