On the critical line zeros of $L$ -- functions attached to automorphic cusp forms

Abstract

We prove for L-function attached to an automorphic cusp form for the Hecke congruence group ${\Gamma }_0(D)$, which is also an eigenfunction of all the Hecke operators, that a positive proportion of its non-trivial zeros lie on the critical line. This result extends the work of J.L. Hafner of 1983 where the case of the full modular group is considered.

20 pages, published in 2010 in Math. Notes