About zero counting of Riemann Z function
Giovanni Lodone
TL;DR
This paper refines estimates of the number of zeros of the Riemann Zeta function using an improved approximation of the Riemann Xi function, enhancing understanding of its zero distribution.
Contribution
It introduces a refined method for counting zeros of the Riemann Zeta function based on an improved approximation of the Riemann Xi function.
Findings
More accurate zero counts up to high imaginary parts
Enhanced understanding of zero distribution patterns
Potential implications for the Riemann Hypothesis
Abstract
An approximate formula for complex Riemann Xi function, previously developed, is used to refine Backlund's estimate of the number of zeros till a chosen imaginary coordinate
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Taxonomy
Topicsadvanced mathematical theories · Meromorphic and Entire Functions · Analytic Number Theory Research