In [this paper](https://arxiv.org/abs/1202.2676), notation $Td\_p$ is used without explicit definition (it is stated that it is a certain combination of Chern numbers). It is claimed that HRR theorem implies
$$
Td\_p(M)=\sum\_{q}(-1)^q h^{p, q}(M)
$$
for any closed complex manifold $M$. 


Am I correct assuming that $Td\_p$ stands for the pairing of $Td(M)Ch(\Omega^p)$ with the fundamental class of $M$? Here $\Omega$ is the canonical bundle.



$Td_p$ notation of Kotschick
The HRR-Theorem asserts $$\int Td(M)ch(E)=\chi(M,E)=\sum\_q(-1)^q\dim H^q(M,E)$$
for every vector bundle $E$. With $E=\Omega^p$ the sheaf of holomorphic $p$-forms you get
$$\int Td(M)ch(\Omega^p)=\sum\_q(-1)^q\dim H^q(M,\Omega^p)=\sum\_q(-1)^q h^{p,q}.$$
So your guess is right.


