What question did this study set out to answer?

The aim is to prove the existence of a unique zero for a function related to the Riemann zeta function.

March 22, 2026Open Access

The Equilibrium Point of the Riemann Zeta Function Between e and π: A Theorem and a New Constant Beq

Key Points

The aim is to prove the existence of a unique zero for a function related to the Riemann zeta function.
Proved the function f(x) = ζ(x) − ζ(e+π−x) has a zero
Analyzed the interval (e, π) for the unique point
Defined the equilibrium constant B_eq at the zero point
Identified x* = (e+π)/2 as the unique zero
Calculated B_eq = ζ((e+π)/2) ≈ 1.21654
Remains uncertain about the arithmetic nature of B_eq

Abstract

We prove that f (x) = ζ (x) − ζ (e+π−x) has a unique zero on (e, π) at x* = (e+π) /2, and define the equilibrium constant Bₑq = ζ ( (e+π) /2) ≈ 1. 21654. . . whose arithmetic nature remains open.

Connected Papers

Building similarity graph...

Analyzing shared references across papers

Discussion

Authors

Judicael Brindel

Actions

Institutions

Progamme National Contre le Tuberculose

References and Citations

Connected Papers

Building similarity graph...

Analyzing shared references across papers

The Equilibrium Point of the Riemann Zeta Function Between e and π: A Theorem and a New Constant Beq

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Authors

Actions

Institutions

References and Citations

Citation Network

Connected Papers

Discussion

Cite this study

Also consider