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