  Stable Khovanov-Rozansky polynomials of algebraic knots are expected to
coincide with certain generating functions, superpolynomials, of nested Hilbert
schemes and flagged Jacobian factors of the corresponding plane curve
singularities. Also, these 3 families conjecturally match the DAHA
superpolynomials. These superpolynomials can be considered as singular
counterparts and generalizations of the Hasse-Weil zeta-functions. We
conjecture that all $a$-coefficients of the DAHA superpolynomials upon the
substitution $q\mapsto qt$ satisfy the Riemann Hypothesis for sufficiently
small $q$ for uncolored algebraic knots, presumably for $q\le 1/2$ as $a=0$.
This can be partially extended to algebraic links at least for $a=0$. Colored
links are also considered, though mostly for rectangle Young diagrams.
Connections with Kapranov's motivic zeta and the Galkin-St\"ohr zeta-functions
are discussed.
