Integral Representations and Arithmetic of Odd Zeta and Even Beta Values

This work investigates the values of the Riemann zeta function at odd positive integers and the Dirichlet beta function at even positive integers. By deriving new classes of definite integrals involving logarithmic, hyperbolic, and trigonometric functions, we obtain new representations and numerical bounds for ζ(2n + 1)/π^(2n+1) and β(2n)/π^(2n). The results suggest deeper arithmetic structures and point towards new conjectures on irrationality and transcendence.