Perspectives on the arithmetic nature of the ratios ζ (2n + 1) /π^2n+1 and β (2n) /π^2n

Key Points

• Irrationality of ζ(2n + 1)/π^{2n+1} and β(2n)/π^{2n} is suggested by the investigation.
• Key focus includes values of the Riemann zeta function at odd integers and their relationships.
• The analysis unites distinct analytic frameworks and presents conjectures that enhance understanding of these mathematical functions.
• Insights gained may lead to significant implications for number theory and mathematical irrationality.