Geodesic
On the Zeros on the Critical Line of $L$-Functions Corresponding to Automorphic Cusp Forms
Matematičeskie zametki, Tome 88 (2010) no. 3, pp. 456-475

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We consider an automorphic cusp form of integer weight $k\ge1$, which is the eigenfunction of all Hecke operators. It is proved that, for the $L$-series whose coefficients correspond to the Fourier coefficients of such an automorphic form, the positive fraction of nontrivial zeros lies on the critical line.
Keywords: automorphic cusp form, Riemann zeta function, Riemann hypothesis, Hecke operator, $L$-function, Jutila's circle method. 
@article{MZM_2010_88_3_a13,
     author = {I. S. Rezvyakova},
     title = {On the {Zeros} on the {Critical} {Line} of $L${-Functions} {Corresponding} to {Automorphic} {Cusp} {Forms}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {456--475},
     publisher = {mathdoc},
     volume = {88},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_3_a13/}
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I. S. Rezvyakova. On the Zeros on the Critical Line of $L$-Functions Corresponding to Automorphic Cusp Forms. Matematičeskie zametki, Tome 88 (2010) no. 3, pp. 456-475. http://geodesic.mathdoc.fr/item/MZM_2010_88_3_a13/