  The goal of this note is to present the potential relationships between
certain Monge-Amp\`ere integrals appearing in holomorphic Morse inequalities,
and asymptotic cohomology estimates for tensor powers of line bundles, as
recently introduced by algebraic geometers. The expected most general
statements are still conjectural and owe a debt to Riemann's pioneering work,
which led to the concept of Hilbert polynomials and to the
Hirzebruch-Riemann-Roch formula during the XX-th century.
