Zero density estimates of L-functions associated with cusp forms
A family of Zeta functions built as Dirichlet series over the Riemann zeros are shown to have meromorphic extensions in the whole complex plane, for which numerous analytical features (the polar structures, plus countably many special values) are explicitly displayed.
This work is about a generalization of Kœcher’s zeta function. Let be an Euclidean simple Jordan algebra of dimension and rank , an Euclidean space of dimension , a regular self-adjoint representation of in , the quadratic form associated to , the symmetric cone associated to and its automorphism group() Assume that and have -structures and respectively and is defined over . Let be a lattice in . The zeta series associated to and is defined bywhere ,...