On the success and failure of Gram's Law and the Rosser Rule

2011/01/01 by Timothy S. Trudgian · 26 citations
Mathematics · #Analytic Number Theory Research #Benford’s Law and Fraud Detection #Advanced Mathematical Identities #Mathematics #Gram #Law #Political science #Geology

paper · pdf · doi:10.4064/aa148-3-2

published in Acta Arithmetica 148(3), 225-256 (Polish Academy of Sciences)

openalex publication_date 2011/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22

Abstract

Gram calculated the first fifteen roots [of the function Z(t)] and called attention to the fact that the 's and the g 's separate each other. I will refer to this property of the roots as Gram's Law.

Citations

• More than two fifths of the zeros of the Riemann zeta function are on the critical line.
• On the value-distribution of the Riemann zeta-function on the critical line
• Exponential sums and the Riemann zeta function v
• Some Calculations of the Riemann Zeta-Function
• On the Zeros of the Riemann Zeta Function in the Critical Strip. IV
• Mean-Value Theorems in the Theory of the Riemann Zeta-Function
• The zeros of the Riemann zeta-function
• On the Distribution of Zeros of the Riemann Zeta-Function
• The zeros of the Riemann zeta-function
• On the Roots of the Riemann Zeta Function

Cited by

• Riemann hypothesis [wikipedia]