The Equilibrium Point of the Riemann Zeta Function Between e and π: A Theorem and a New Constant Beq | Synapse
March 22, 2026Open Access
The Equilibrium Point of the Riemann Zeta Function Between e and π: A Theorem and a New Constant Beq
Puntos clave
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
Resumen
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.