  Odd-frequency Cooper pairs with chiral symmetry emerging at the edges of
topological superconductors are a useful physical quantity for characterizing
the topological properties of these materials. In this work, we show that the
odd-frequency Cooper pair amplitudes can be expressed by a winding number
extended to a nonzero frequency, which is called a `spectral bulk-boundary
correspondence,' and can be evaluated from the spectral features of the bulk.
The odd-frequency Cooper pair amplitudes are classified into two categories:
the amplitudes in the first category have the singular functional form $\sim
1/z$ (where $z$ is a complex frequency) that reflects the presence of a
topological surface Andreev bound state, whereas the amplitudes in the second
category have the regular form $\sim z$ and are regarded as non-topological. We
discuss the topological phase transition by using the coefficient in the latter
category, which undergoes a power-law divergence at the topological phase
transition point and is used to indicate the distance to the critical point.
These concepts are established based on several concrete models, including a
Rashba nanowire system that is promising for realizing Majorana fermions.
