Virtual homological eigenvalues and the Weil-Petersson translation length

For any pseudo-Anosov automorphism on an orientable closed surface, inequality is established by bounding certain growth of virtual homological eigenvalues with the Weil-Petersson translation length. The new fits nicely other known inequalities due to Kojima and McShane (2018) Lê (2014). quantity be considered square sum logarithmic radii (with multiplicity) outside complex unit circle, called Jensen sum. main theorem as follows. cofinal sequence regular finite covers a given together lifts pseudo-Anosov, grows at most linearly fast compared covering degree, root rate $$1/\sqrt {4\pi } $$ times length pseudo-Anosov.