Explicit extreme values of the argument of the Riemann zeta-function

2025/10/16 by Inoue, Shōta, Kobayashi, Hirotaka, Toma, Yuichiro
#11M06 #11M26 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2510.14309

Abstract

We investigate explicit extreme values of the argument of the Riemann zeta-function in short intervals. As an application, we improve the result of Conrey and Turnage-Butterbaugh concerning r-gaps between zeros of the Riemann zeta-function.

Citations

• A note on r-gaps between zeros of the Riemann zeta-function
• On the Montgomery-Odlyzko method regarding gaps between zeros of the zeta-function
• Extreme values of zeta and L-functions

Related

• On gaps between zeros of the Riemann zeta function
• Gaps between zeros of the Riemann zeta-function
• On large gaps between zeros of the Riemann zeta-function
• Large gaps between consecutive zeros of the Riemann zeta-function. II
• Unconditional and Conditional Large Gaps between the zeros of the Riemann Zeta-Function