A note on S(T) and the zeros of the Riemann zeta-function
Reviewed by Pithpith:2UCXPM7Copen to challenge →
read the original abstract
Let $\pi S(t)$ denote the argument of the Riemann zeta-function at the point $\frac12+it$. Assuming the Riemann Hypothesis, we sharpen the constant in the best currently known bounds for $S(t)$ and for the change of $S(t)$ in intervals. We then deduce estimates for the largest multiplicity of a zero of the zeta-function and for the largest gap between the zeros.
This paper has not been read by Pith yet.
Forward citations
Cited by 2 Pith papers
-
Spectral Riccati--Gamma Concavity, Symmetric Zero Cancellation, and Conditional Criteria for the Riemann Hypothesis
Rules out naive concavity criterion for RH and derives conditional zero-density and localisation criteria via a finite spectral Riccati-Gamma averaging framework.
-
Spectral Riccati--Gamma Concavity, Symmetric Zero Cancellation, and Conditional Criteria for the Riemann Hypothesis
Develops a Riccati-Gamma spectral averaging method for the completed zeta log derivative, proves cancellation and conditional positivity properties, and isolates verifiable assumptions that would imply the Riemann Hypothesis.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.