This paper systematically deepens the rapidly convergent summation formulas for the Riemann zeta function in the complex order and multivariable settings, and uses them as core tools to construct an interdisciplinary research framework for studying the Riemann Hypothesis and related problems. We first give a rigorous proof of the uniform convergence of the rapid convergence formula on the right half plane, and derive its precise remainder estimate based on Stirling’s formula for the Gamma function.On this basis, we propose a novel analytic equivalent form of the Riemann Hypothesis and, through fine asymptotic analysis, provide a proof path that reduces the problem to finite computational verification.To further explore the nature of zero distribution, we strictly define an integral operator on Hilbert space associated with the spectrum of zeta function zeros, and formalize the spectral correspondence conjecture. We extend the rapid convergence method to double zeta functions, providing an efficient algorithmic foundation for related numerical computations. The paper also outlines the principle of large-scale zero verification based on rigorous interval arithmetic and discusses its potential theoretical applications in cryptography and quantum computing. This study aims to provide new theoretical tools and interdisciplinary perspectives for the exploration of the Riemann Hypothesis.
shifa liu (Wed,) studied this question.