Correcting Lehman’s theorem on Turing’s method

2024/01/17 by Nuno Pereira
Computer Science · #Computability, Logic, AI Algorithms

paper · doi:10.1090/mcom/3946

Abstract

We show that there is an error in a theorem by Lehman, which has been used to apply Turing’s method for estimating the number of zeros of the Riemann zeta function in the critical strip. The constants in Lehman’s theorem must be doubled and this implies changes in some formulas that were deduced from that theorem.

Citations

• Improvements to Turing’s method
• On the Distribution of Zeros of the Riemann Zeta-Function
• An improved explicit estimate for ζ(1/2 + it)

Related

• Improvements to Turing's Method II
• On the zeros of the Riemann zeta function
• Improvements to Turing’s method
• A positive answer to the Riemann hypothesis: A new result predicting the\n location of zeros
• Improved estimates for the argument and zero-counting of Riemann zeta-function