Dice Question Streamline Icon: https://streamlinehq.com

Exact value of the constant C2 in the Murty–Murty M2(x) conjecture

Determine whether the constant C2 appearing in the conjectured asymptotic M2(x) ∼ C2·log x equals ζ(2)^2·ζ(3)/ζ(6), where ζ denotes the Riemann zeta function.

Information Square Streamline Icon: https://streamlinehq.com

Background

Identifying the constant C2 would fully resolve the second moment conjecture and link the distribution of ω*(n) to values of the Riemann zeta function, reflecting deep multiplicative structure.

This conjectured identity for C2 arises from heuristic arguments and would represent a precise quantitative refinement of the Murty–Murty conjecture.

References

Based on a heuristic argument, the first author also conjectured that $C_2=\zeta(2)2\zeta(3)/\zeta(6)$, where $\zeta$ is the Riemann zeta-function.

— The maximal order of the shifted-prime divisor function (2510.14167 - Fan et al., 15 Oct 2025) in Section 1 (Introduction)