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

Publication date: 12 December 2012

Abstract: We prove for L-function attached to an automorphic cusp form for the Hecke congruence group

G a m m a_{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.

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