Supremum of the function S₁(t) on short intervals

2013/01/01 by Takahiro Wakasa, Wakasa, Takahiro
Mathematics · #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical and Theoretical Analysis #Number Theory (math.NT) #advanced mathematical theories #math.NT

paper · pdf · doi:10.48550/arxiv.1301.0057

15 pages

openalex publication_date 2013/01/01 · arxiv created 2013/11/18 · arxiv updated 2013/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a lower bound on the supremum of the function S₁(T) on short intervals, defined by the integration of the argument of the Riemann zeta-function. The same type of result on the supremum of S(T) have already been obtained by Karatsuba and Korolev. Our result is based on the idea of the paper of Karatsuba and Korolev. Also, we show an improved Omega-result for a lower bound.

Related

• Upper and lower bounds for the function S(t) on the short intervals
• Universality of the zeta function in short intervals
• The explicit upper bound of the multiple integral of S(t) on the Riemann Hypothesis
• Effective Weak Universality in Short Intervals
• Explicit extreme values of the argument of the Riemann zeta-function