This article presents a new method to calculate eigenvalues of right triangle
billiards. Its efficiency is comparable to the boundary integral method and
more recently developed variants. Its simplicity and explicitness however allow
new insight into the statistical properties of the spectra. We analyse
numerically the correlations in level sequences at high level numbers (>10^5)
for several examples of right triangle billiards. We find that the strength of
the correlations is closely related to the genus of the invariant surface of
the classical billiard flow. Surprisingly, the genus plays and important role
on the quantum level also. Based on this observation a mechanism is discussed,
which may explain the particular quantum-classical correspondence in right
triangle billiards. Though this class of systems is rather small, it contains
examples for integrable, pseudo integrable, and non integrable (ergodic,
mixing) dynamics, so that the results might be relevant in a more general
context.Comment: 18 pages, 8 eps-figures, revised: stylistic changes, improved
presentatio